# Find the number of terms in each of the following APs:

i) 7, 13, 19,..., 205

ii) 18, 15 ½, 13 ,..., -47

**Solution:**

The formula for n^{th} term of an AP is a_{n} = a + (n - 1) d

Here, a_{n} is the n^{th} term, a is the first term, d is the common difference and n is the number of terms.

(i) 7, 13, 19,..., 205

a = 7

d = 13 - 7 = 6

a_{n} = 205

a_{n} = a + (n - 1)d

a + (n - 1)d = 205

7 + (n - 1) 6 = 205

(n - 1) 6 = 205 - 7

(n - 1) 6 = 198

n - 1 = 33

Answer: Number of terms in the given Arithmetic Progression is 34.

ii) 18, 15 ½, 13 ,..., -47

d = 15 ½ - 18

= 31/2 - 18

= - 5/2

a_{n} = a + (n - 1)d

- 47 = a + (n - 1) d

- 47 = 18 + (n - 1) (- 5 / 2)

- 65 = - 5/ 2 n + 5 / 2

5/ 2 n = 5 / 2 + 65

5 / 2 n = 135 / 2

n = 135 / 2 × 2 / 5

= 27

Answer: The number of terms in the given AP is 27.

**Video Solution:**

## Find the number of terms in each of the following APs: i) 7, 13, 19,..., 205 ii) 18, 15 ½, 13 ,..., -47

### NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 5 - Chapter 5 Exercise 5.2 Question 5:

Find the number of terms in each of the following APs: i) 7, 13, 19,..., 205 ii) 18, 15 ½, 13 ,..., -47

The number of terms in the APs 7, 13, 19,……,205 and 18, 15½, 13,…,−47 are 34 and 27 respectively