Question 1 :
Find the sum of the odd numbers between 0 and 50.
Question 2 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 3 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 4 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 5 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 6 :
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 7 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 8 :
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 9 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.
Question 10 :
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 11 :
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
Question 12 : <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 13 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 14 :
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 15 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Question 16 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 17 :
In an AP, given $a = 3, n = 8, S = 192$, find d.
Question 19 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 20 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 21 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 22 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Question 23 :
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 24 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.
Question 25 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Question 26 :
In an AP, given $a = 2, d = 8, S_n = 90$, find n and $a_n$.
Question 27 :
Find the sum of the first 15 terms in $a_n = 9 – 5n$
Question 28 :
In the following AP, find the missing term: 2, __ ,26
Question 29 : <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 30 : <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 31 :
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 32 : <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 33 :
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Question 34 : <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 35 :
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Question 36 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.
Question 37 :
30th term of the AP: 10, 7, 4, . . . , is
Question 38 :
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 39 :
11th term of the AP: – 3, -0.5, 2, . . ., is
Question 40 :
Find the sum of the first 40 positive integers divisible by 6.
Question 41 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Question 42 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Question 43 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 44 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 46 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 9 – 5n$?
Question 47 :
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 48 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 49 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?
Question 50 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
