Question 1 :
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?

Question 2 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.

Question 3 :
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 4 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?

Question 5 :
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 6 :
<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 7 :
In an AP, given $a = 3, n = 8, S = 192$, find d.

Question 9 :
<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 10 :
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 11 :
Find the sum of the first 15 terms in $a_n = 9 – 5n$

Question 12 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.

Question 13 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.

Question 14 :
Find the sum of the odd numbers between 0 and 50.

Question 15 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?

Question 17 :
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 18 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 2nd term ?

Question 19 :
<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 20 :
Find the sum of the first 40 positive integers divisible by 6.

Question 21 :
<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 22 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?

Question 23 :
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 24 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

Question 25 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.

Question 26 :
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 27 :
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 28 :
11th term of the AP: – 3, -0.5, 2, . . ., is

Question 29 :
30th term of the AP: 10, 7, 4, . . . , is

Question 30 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10