Question 1 : <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 2 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Question 3 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.
Question 4 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?
Question 5 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10
Question 6 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 7 :
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Question 8 :
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 9 :
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 10 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?
Question 12 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 13 :
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 14 :
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Question 15 :
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Question 16 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?
Question 17 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Question 18 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.
Question 19 : <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 20 :
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 21 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?
Question 23 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 24 : <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 25 :
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 26 :
Find the sum of the odd numbers between 0 and 50.
Question 27 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Question 28 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 29 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?
Question 30 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 3 + 4n$?
Question 31 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.
Question 32 : <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 33 :
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Question 34 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.
Question 35 :
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 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 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Question 38 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 39 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.
Question 40 :
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 41 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.
Question 42 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 43 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.
Question 44 :
In an AP, given $a = 2, d = 8, S_n = 90$, find n and $a_n$.
Question 45 :
Find the sum of the following AP: –37, –33, –29, . . ., to 12 terms.
Question 46 :
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Question 47 :
In the following AP, find the missing term: 2, __ ,26
Question 48 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 49 :
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 50 :
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.
