Question

Find the number of terms in the following A.P.

`18, 15 1/2, 13`, ..., – 47

How many terms are there in the AP?

`18, 15 1/2, 13`, ..., -47

Answer 1

For this A.P.

a = 18

`d = a_2 - a_1 = 15 1/2 - 18`

`d = (31 - 36)/2 = -5/2`

Let there are n terms in this A.P.

Therefore, a_n = –47 and we know that,

a_n = a + (n – 1)d

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

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

`-65 = (n - 1)(-5/2)`

`(n - 1) = - 65 xx (-2/5)`

(n – 1) = 26

n = 26 + 1

n = 27

Thus, the required number of terms is 27.