Question 1 :
11th term of the AP: – 3, -0.5, 2, . . ., is
Question 2 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 3 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 4 :
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
Question 5 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 6 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 7 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.
Question 8 :
In an AP, given $a = 3, n = 8, S = 192$, find d.
Question 9 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.
Question 10 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 11 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Question 12 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 14 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 15 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 16 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Question 17 :
30th term of the AP: 10, 7, 4, . . . , is
Question 18 :
In an AP, given $d = 5, S_9 = 75$, find a and $a_9$.
Question 19 :
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Question 20 :
Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000?
Question 21 :
Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.
Question 22 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 23 :
Find the sum of the first 40 positive integers divisible by 6.
Question 24 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Question 25 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc6273b230584979a13.JPG' />
In the above fig. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in above figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc9273b230584979a16.JPG' />
In the above fig. A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are $2\frac{1}{2}$ m apart, what is the length of the wood required for the rungs?
Question 27 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 28 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc9273b230584979a17.JPG' />
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 0.25 m and a tread of 0.5 m. Calculate the total volume of concrete required to build the terrace.
Question 29 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc3273b230584979a0e.JPG' />
In the above fig, find the missing value corresponding to (iii)
Question 31 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 32 :
In an AP, given $a = 2, d = 8, S_n = 90$, find n and $a_n$.
Question 33 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.
Question 34 :
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum offirst n terms.
Question 35 :
Find the sum of the following AP: –37, –33, –29, . . ., to 12 terms.
Question 36 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 37 :
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Question 38 :
In the following AP, find the missing term: 2, __ ,26
Question 39 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.
Question 40 :
The sum of the third and the seventh termsof an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Question 41 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 42 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.
Question 43 :
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Question 44 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?
Question 45 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, what is the sum of the AP?
Question 46 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 47 :
Find the sum of the odd numbers between 0 and 50.
Question 48 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.
Question 49 :
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
