Question 1 :
The 17th term of the series 3 + 7 + 11 + 15 + ......... is :
Question 2 :
If the sum of $n$ terms of an A.P. is $nA+{n}^{2}B$, where $A,B$ are constants, then its common difference will be
Question 3 :
5th term of an AP is 26 and 10th term is 51. The 15th term is :
Question 5 :
If there are '$n$' arithmetic means between $a$ and $b$, then the common difference $(d)=$
Question 6 :
If $a, b, c$ are in A.P. then $\dfrac {a - b}{b - c}$ is equal to
Question 8 :
Which term of the sequence 4, 9, 14, 19, ... is 124 ?
Question 9 :
If $a, b, c$ are in A.P., then $a^2+4b^3 + c^3$ is equal to ______. 
Question 10 :
Which of the following is not in the form of G.P.?<br>
Question 12 :
The number of terms in a sequence $6, 12, 24, ....1536$ represents a<br/>
Question 13 :
Find the first three terms of the A.P. whose first term is 2/3 and common difference is 1/3?
Question 14 :
The sum of 3 numbers in an AP is 111, and the differences of the squares of the greatest and least is 1776.The smallest number is
Question 16 :
Which term of an A.P : 21, 42, 63,.... is 210 ?<br/>
Question 17 :
In a _______ each term is found by multiplying the previous term by a constant.<br>
Question 18 :
What is the first four terms of the A.P. whose first term is $3$ and common difference is $5$?
Question 19 :
The common difference of an A.P. is 10, then what is $a_2 - a_5$?
Question 20 :
Number of identical terms in the sequence $2, 5, 8, 11....$ upto $100$ terms are
Question 21 :
The first and the last term of A.P. are $7$ and $630$ respectively. If the common difference is $7$, how many terms are there and what is their sum?
Question 23 :
In an AP, if $d=-2,n=5$ and $a_{n}=0$, then the value of $a$ is <br/>
Question 24 :
The sum of the first five terms and the sum of the first ten terms of an AP are same. Which one of the following is the correct statement?
Question 25 :
Which term of an AP: 2, -1, - 4, ...................... is - 70?<br/>
Question 27 :
If $p, q$ and $r$ are in A. P. then which of the following statements is correct?
Question 29 : Find the first term of the sequence whose $n^{th}$ is given as:<div>$t_n\,=\,4n\,-\,3$</div>
Question 30 :
Let $a_n$ be an A.P. for which $d = 8$ and $a_2 = 12$. Find $a_1$
Question 32 :
Find the first term and common difference in the A.P. $1 + 2 + 3 + 4 +$ ........
Question 34 :
For what value of $p$ are $2p + 1, \ 13, \ 5p - 3,$ three consecutive terms of an A.P. ?<br/>
Question 35 :
Which one of the following is a general form of geometric progression?<br>
Question 36 :
<span>The $11^{th}$ term and the $21^{st}$ term of an A.P. are $16$ and $29$ respectively, then the </span><span>$1^{st}$ term is:</span>
Question 37 :
Split $69$ late three pats such that they are in $A.P.$ and the product of two smaller parts is $483$.
Question 38 :
The first four terms of an $A.P.$ whose first term is $2$ and the common difference is $2$ are:<br/>
Question 39 :
If $11$ $AM.s$ are inserated between $28$ and $10$, then the middle term in the series is
Question 40 :
Find the difference between the sum of all even numbers from $1$ to $1000$ and the sum of all odd numbers from $1$ to $1000$.
Question 41 :
If the 2nd and the 6th term of an A.P. are 8 and 20 respectively. Which term of this A.P. is five?
Question 42 :
An Arithmetic progression consists of 20 terms of which 4th term is 16 and the last term is 208. Find the 15th term
Question 43 :
<span>If a, b, c are in A.P., then </span><span>$\dfrac{1}{bc}, \dfrac{1}{ca}, \dfrac{1}{ab}$ are in</span>
Question 44 :
A sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence is known as<br/>
Question 45 :
If the common difference of an A.P. is $3$, then $a_{20}-a_{15}$ is<br/>
Question 46 :
Mean of the first $n$ terms of the A.P. $a, (a + d), (a + 2d), ........$ is
Question 47 :
Find the number of terms in an arithmetic progression with the first term $2$ and the last term being $62,$ given that common difference is $2$
Question 48 :
Find $a_n$ where $n = 10, d = 15$ and $a = 20$
Question 49 :
The sum of six consecutive numbers is $150$. Find the first number
Question 50 :
Let $m$ and $n$ $(m<n)$ be the roots of the equation $x^2-16x+39=0$. If four terms $p,q,r$ and $s$ are inserted between $m$ and $n$ form an $AP$, then what is the value of $p+q+r+s?$
Question 52 :
The sum of the first 55 terms of an A.P. is 3300. Find the $28^{th}$ term.
Question 54 :
In a given AP., if the p term is 'q' and the $q^{th}$ tent is 'p', then its $n^{th}$ term is _______.
Question 55 :
<span>If the sum of the first n terms of an A.P. is given by the equation $n^2 + 7n$, then what is the first term and second term?</span>
Question 56 :
Find the number of terms common to the two A,P's $3,7,11,.....,407$ and $2,9,16,..........,709$
Question 57 :
What is the number of terms in the series $117, 120, 123, 126,.., 333$ ?
Question 59 :
If the nth term of a progression be a linear epression in n, then the given progression is
Question 61 :
The sum of 2nd and 4th term of an A.P. is 11 and the sum of the 5th and 10th terms is 20. Find the first three terms of the A.P.
Question 62 :
The ratio of the sum to $n$ terms of two $A.P's$ is $(7n+1)(4n+27)$. Then the ratio of their $m^{th}$ terms is ?<br/>
Question 63 :
If $ S_n=nP+\frac{n}{2}(n-1)Q,$ where $S_n$ denotes the sum of the first $n$ terms of an A.P., then the common difference is<br>
Question 64 :
Let s$_1$ ,s$_2$, s$_3$ be the sums of n term of each being 1 and the common differences 1, 2,3 respectively. If s$_1$ + s$_3$ = $\lambda$ <span>s$_2$, then the value of $\lambda$ is</span>
Question 65 :
Which term of the AP $24, 21, 18, ..............$ is the first negative term. ?<br/>
Question 66 :
Three numbers are in arithmetic progression. Their sum is $21$ and the product of the first number and the third number is $45$. Then the product of these three number is
Question 67 :
<span>If the sum of the first $15$ terms of an A.P. is given by the equation $2n - n^2 + 1$, then what is their first term?</span>
Question 68 :
If $a^2(b+c),b^2(c+a), c^2(a+b)$<span> are in AP, then $a, b, c$ are in</span>
Question 69 :
The first term of an A.P. is 6, the last term is 42 and the sum is 600. Find the number of terms.
Question 70 :
If $\begin{vmatrix}x\end{vmatrix}< 1$ then the coefficient of  $x^{3}$  in the expansion of  $\dfrac{3x}{(x-2)(x+1)}$ is <br/>
Question 71 : <p>Let ${A_1}$ denotes arithmetic mean of two numbers $a=1$b=2. $ {A_2}$ denotes arithmetic mean of $ {A_1}$ and $b$. For $n \ge 3$,let ${A_n}$ is arithmetic mean of ${A_n}_{ - 1}$ and $b$ , then</p>
Question 72 :
In a triangle, the angle are in AP and the length of the two larger sides are $10$ and $9$ respectively, then the length of the third side can be
Question 73 :
If $log_{10} a, log_{10}, log_{10} c$ are in A.P., then $a, b, c$ must be in<br>
Question 74 :
The angles $A, B$ and $C$ of a triangle $ABC$ are in $A.P.$ If $b : c = \sqrt {3} : \sqrt {2}$, then the angle $A$ is
Question 75 :
An A.P. consists of $13$ terms of which $2^{nd}$ terms is $10$ and the last term is $120$. Find the $9^{th}$ term.
Question 76 :
An AP consists of $23$ terms. If the sum of the $3$ terms in the middle is $141$ and the sum of the last $3$ terms is $261$, then the first term is
Question 77 :
If $3 +(3 + d) +(3 + 2d) = 15$, then the value of $d$ is
Question 78 :
The sum of 'n' terms of two A.P.'s are in the ratio of $\dfrac {5n + 2}{11n - 7}$. Find the ratio of their sixth terms.
Question 80 :
Find the $21^{st}$ term of an A.P. whose $1^{st}$ term is $8$ and the $15^{th}$ term is $120$.
Question 81 :
If four numbers are in A.P. such that their sum is 60 and the greatest number is 4 times the least, then the numbers are ______.
Question 82 :
If the sum of p terms of an A. P. is q and the sum of q terms is p, then the sum of <span>p + q terms is ______.</span>
Question 83 :
If the coefficient of second, third and fourth terms in the expansion if $(1+x)^{2n}$ are in A.P, the $2n^2-3n$ is equal to
Question 84 :
If $a,b,c$ are distinct  and the roots of $\left( b-c \right) { x }^{ 2 }+(c-a)x+(a+b)=0$ are equal, then<b> </b>$a,b,c$ are in
Question 85 :
Let $a_{1}, a_{2}, ...., a_{10}$ be in $AP$ and $h_{1}, h_{2}, ...., h_{10}$ be in $HP$. If $a_{1} = h_{1} = 2$ and $a_{10} = h_{10} = 3$. Then, $a_{4}h_{7}$ is
Question 86 :
What is the common difference of an AP in which the ratio of the product of the first and fourth term to the product of the second and third term is $2:3?$ It is given that the sum of the four terms is $20.$
Question 87 :
If $m$ arithmetic means are inserted between $1$ and $31$, so that the ratio of the $7^{th}$ and $(m-1)^{th}$ means is $5 : 9$, then the value of $m$ is<br/>
Question 88 :
<span>Suppose $a_{1},a_{2},a_{3}........a_{2012} $<span> <span>are integers <span>arranged <span>on a <span>circle.Each number is equal to <span>the average of its <span>two adjacent numbers. If the sum of all even indexed numbers is $3018$,what is the sum of all numbers?</span></span></span></span></span></span></span></span><br/>
Question 89 :
The $30th$ term of the arithmetic progression $10, 7 , 4$ is
Question 90 :
If the sums of n, 2n and 3n terms of an A.P. are $S_1, S_2$ and $S_3$ respectively, then $\frac {s_3}{(s_2-s_1)}$ is _____.
Question 91 :
For any three positive real numbers a, b and c, $9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c)$. Then.
Question 92 :
<span>The sum of two numbers is $2\dfrac {1}{6}$. If an even number of arithmetic means are inserted between them and their sum exceeds their number by $1,$ then number of means inserted is</span><br/>
Question 93 :
If there are $11$ arithmetic means between $20$ and $80$, identify the value of the fourth mean.
Question 94 :
In an A.P of which $a$ is the first term, if the sum of the first $p$ terms is zero, then the sum of the next $q$ term is:
Question 95 :
Three numbers $x, y$ and $z$ are in arithmetic progressions. If $x + y + z = -3$ and $xyz = 8$, then $x^2 + y^2 + z^2$ is equal to
Question 97 :
Let $s_1$ (n) be the sum of the first n terms of the arithmetic progression 8, 12, 16,..... and let $s_2$ (n) be the sum of the first n terms of arithmetic progression 17, 19,21 ..... If for some value of n, $s_1(n) =s_2(n)$ then this common sum is
Question 98 :
If $a,\dfrac{1}{b}, c\ and\ \dfrac{1}{p},q,\dfrac{1}{r}$ form two arithmetic progressions of the same common difference, then $a,q,c$ are in $A.P.$ if
Question 99 :
If the $p^{th}, q^{th}$ and $r^{th}$ terms of an A. P. are P, Q, R respectively, then $P(q-r) + Q(r-p) + R (p-q) $ equals ______.
Question 101 :
If $2(a-b) + x(b-c)^2 + (c-a)^3 = 2(a-d) + (b-d)^2 + (c-d)^3$ where a,b,c are four distinct real numbers and they are in A.P., then the possible value of $x$ can be
Question 102 :
a, b, c are distinct real number such that a, b, c are in A. P. and and a$^2$, b$^2$, c$^2$ are in H. P. then
Question 103 :
Let $S_{n}$ denotes the sum of first $n$ terms of an $A.P$. If $S_{2n}=3\ S_{n}$, then the ratio $S_{3n}/S_{n}$ is equal to
Question 104 :
Let $a_1, a$ and $b_1, b_2, ....$ be the arithmetic progressions such that $a_1 = 25, b_1 = 75$ and $a_100+b_{100}$. The sum of the first one hundred terms of the progressions $(a_1+b_1), (a_2 +b_2)$, ...... is _______.
Question 105 : <span>Match the statements in List 1 with those in List 2</span><br/><table class="wysiwyg-table"><tbody><tr><td></td><td><b>List 1</b></td><td></td><td><b>List 2</b></td></tr><tr><td>A.</td><td><span>Sum of $n$ A.M.'s between a and b is</span><br/></td><td>1.</td><td><span>$(\sqrt{ab})^n$</span><br/></td></tr><tr><td>B.</td><td><span>Product of $n$ G.M.'s between a and b is</span><br/></td><td>2.</td><td><span>$2A \,pq$</span><br/></td></tr><tr><td>C.</td><td><span>If A, G, H are A.M., G.M., H.M, between the same two numbers, such that $A - G = 15$ and $A - H = 27$, then the numbers are</span><br/></td><td>3.</td><td><span>$\dfrac{G_1G_2}{H_1H_2}$</span><br/></td></tr><tr><td>D.</td><td>$A_1, A_2, G_1,G_2$ and $H_1, H_2$ are respective two A.M.'s two G.M's and two H.M.'s between the same two numbers, then $\dfrac{A_1 + A_2}{H_1 + H_2} =$</td><td>4.</td><td><span>$\dfrac{n(a + b)}{2}$</span><br/></td></tr><tr><td></td><td></td><td>5.</td><td><span>120, 30</span><br/></td></tr></tbody></table><br/>
Question 106 :
If $log_5 \,2, log_5 (2^x - 3)$ and $log_5 \left(\dfrac{17}{2} + 2^{x-1}\right)$ are in AP, then the value of $x$ is
Question 107 :
If the sum of four number in $A.P.$ be $48$ and that the product of the extremes is to the product of the means is $27$ to $35$ then the number are-
Question 108 :
The average expenditure of Sharma for the January to June is Rs. 4200 and he spent Rs. 1200 in January and Rs.1500 in July. The average expenditure for the months of February to July is:
Question 109 :
In a triangle the lengths of two larger sides are $10$ and $9$ respectively. If the angles are in $A.P$ then the length of the third side is
Question 110 :
If $T_{0}, T_{1}, T_{2}, ....., T_{n}$ represent the terms in $(x + a)^{n}$, then $(T_{0} - T_{2} + T_{4} - T_{6} + ....)^{2} + (T_{1} - T_{3} + T_{5} - .....)^{2}$ is
Question 111 :
If $S_{n}=n^{2}p+\displaystyle \frac{n(n-1)}{4}q$ be the sum to $'n'$ terms of an A.P., then the common difference of the A.P. is <br/>
Question 112 :
If three positive numbers $a,b$ and $c$ are in $A.P$. Such that $abc=8$, then the minimum possible value of $b$ is
Question 113 :
The first and last terms of an A.P. are $1$ and $11$. If the sum of its terms is $36$, then the number of terms will be
Question 114 :
If the sum of the roots of the equation $ax^{2} + bx + c = 0$ is equal to sum of the squares of their reciprocals, then $bc^{2}, ca^{2}, ab^{2}$ are in
Question 115 :
if 'l' is the last term of an arithmetic progresson with common difference 'd' then nth term from end is____
Question 116 :
If $S_n=n^2p$ and $S_m=m^2p$, $m\neq n$, in A.P., then $S_p$ is?
Question 117 :
Let ${ \left( 1+{ x }^{ 2 } \right) }^{ 2 }{ \left( 1+x \right) }^{ n }={ A }_{ 0 }+{ A }_{ 1 }x+{ A }_{ 2 }{ x }^{ 2 }+.....$. If ${A}_{0},{A}_{1},{A}_{2}$ are in A.P then the value of $n$ is-
Question 118 :
The distances of three points on a pole from its foot are in A.P. If the angles of elevation of these points from a point on the ground are $\alpha, \beta$ and $\gamma$, then
