Question 1 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.

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

Question 4 :
<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 5 :
Find the sum of the first 15 terms in $a_n = 3 + 4n$.

Question 6 :
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 7 :
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 8 :
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 9 :
Find the number of terms in the following AP :18, 15.5, 13, . . . , – 47

Question 10 :
In an AP, given a = 5, d = 3, $a_n$= 50, find n and $S_n$.

Question 11 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 9 – 5n$?

Question 12 :
In an AP, given $d = 5, S_9 = 75$, find a and $a_9$.

Question 13 :
Which term of the AP : 121, 117, 113, . . ., is its first negative term?

Question 14 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

Question 15 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?

Question 16 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the nth term ?

Question 17 :
<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 19 :
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 20 :
Find the sum of the first 40 positive integers divisible by 6.