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,

an = a + (n − 1) d

-47 = `18 + (n - 1) (-5/2)`

-47 - 18 = `(n - 1) (-5/2)`

-65 = `(n - 1)(-5/2)`

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

(n - 1) = 26

n = 26 + 1

n = 27

Thus, the required number of terms is 27.