Question 1 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc8273b230584979a15.JPG' />
In the above fig. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
Question 3 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Question 4 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 5 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?
Question 6 :
If the sum of the first n terms of an AP is $4n – n^2$, what is the first term (that is $S_1$)?
Question 7 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?
Question 8 : <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 9 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 10 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 11 :
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 12 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 13 :
Find the sum of the odd numbers between 0 and 50.
Question 14 :
Find the number of terms in the following AP :18, 15.5, 13, . . . , – 47
Question 15 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.
Question 16 :
A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the smallest value of the prize.
Question 18 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.
Question 19 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 20 :
In an AP, given $d = 5, S_9 = 75$, find a and $a_9$.
Question 22 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10
Question 23 :
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 24 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.
Question 25 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.
Question 26 :
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 27 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.
Question 28 :
In an AP, given $a = 3, n = 8, S = 192$, find d.
Question 29 :
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?
Question 30 :
In the following AP, find the missing term: 2, __ ,26
Question 31 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.
Question 33 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Question 34 : <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 35 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 36 :
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 37 :
30th term of the AP: 10, 7, 4, . . . , is
Question 38 :
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Question 39 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Question 40 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there in the AP?
Question 41 :
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 42 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 43 :
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 44 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Question 45 :
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 46 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 47 :
Find the sum of the following AP: –37, –33, –29, . . ., to 12 terms.
Question 48 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.
Question 49 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 50 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
