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

Question 2 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.

Question 3 :
<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 4 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?

Question 6 :
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 7 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.

Question 8 :
Find the sum of the following AP: –37, –33, –29, . . ., to 12 terms.

Question 9 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

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

Question 11 :
In an AP, given $a_{12} = 37, d = 3$, find a and $S_{12}$.

Question 12 :
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 13 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.

Question 14 :
Find the sum of the following AP: 34 + 32 + 30 + . . . + 10

Question 15 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84

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 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)

Question 18 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.

Question 19 :
Find the number of terms in the following AP :18, 15.5, 13, . . . , – 47

Question 20 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

Question 21 :
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

Question 22 :
<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 23 :
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?

Question 24 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .

Question 25 :
If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?