Question 1 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 2 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 3 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 4 :
In an AP, given $a = 2, d = 8, S_n = 90$, find n and $a_n$.
Question 5 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 9 – 5n$?
Question 6 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Question 8 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 9 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 10 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 11 :
In an AP, given $d = 5, S_9 = 75$, find a and $a_9$.
Question 12 :
In the following AP, find the missing term: 2, __ ,26
Question 13 : <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 14 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 15 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 16 : <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 17 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.
Question 18 :
30th term of the AP: 10, 7, 4, . . . , is
Question 19 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.
Question 20 :
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 21 :
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 23 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 24 :
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 25 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Question 26 :
Find the sum of the following AP: –37, –33, –29, . . ., to 12 terms.
Question 27 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc4273b230584979a10.JPG' />
In the above fig, find the missing value corresponding to (i)
Question 28 : <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 29 :
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 30 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 31 :
Find the sum of the first 15 terms in $a_n = 9 – 5n$
Question 32 :
Find the sum of the following AP: –37, –33, –29, . . ., to 12 terms.
Question 33 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 34 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 35 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 36 : <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 37 :
30th term of the AP: 10, 7, 4, . . . , is
Question 38 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 39 :
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 40 :
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Question 41 :
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 42 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 43 :
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 44 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 45 :
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 46 :
In the following AP, find the missing term: 2, __ ,26
Question 47 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 48 :
11th term of the AP: – 3, -0.5, 2, . . ., is
Question 49 :
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Question 50 :
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 52 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 53 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc7273b230584979a14.JPG' />
In the above fig. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?
Question 54 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.
Question 56 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.
Question 57 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?
Question 58 : <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 59 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc4273b230584979a10.JPG' />
In the above fig, find the missing value corresponding to (i)
Question 60 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.
