#### Class 10

#### Arithmetic Progressions

#### Exercise 5.2

1. Fill in the blanks in the following table, given that *a *is the first term, *d *the common difference and \(*a_**n\) *the *n*th term of the AP:

2. Choose the correct choice in the following and justify:

(i) 30th term of the AP: 10, 7, 4, . . . , is

(ii) 11^{th} term of the A.P.: \(-3, -\frac{1}{2}, 2, …\) is:

3. In the following APs, find the missing terms in the boxes:

4. Which term of the AP : 3, 8, 13, 18, . . . ,is 78?

5. Find the number of terms in each of the following APs:

(ii) 18, \(15\frac{1}{2}\), 13, …, -47

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

7. Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

8. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

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

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

11. Which term of the AP: 3, 15, 27, 39, . . . will be 132 more than its 54th term?

13. How many three-digit numbers are divisible by 7?

14. How many multiples of 4 lie between 10 and 250?

15. For what value of *n*, are the *n*th terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?

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

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