How many terms are there in the AP 18, 15 , 13, ..., - 47?

Question

Philoid · Accepted Answer

In the given AP, the first term = a = 18

Common difference = d = (31/2) - 18 = (-5/2)

Last term = - 47

To find: No. of terms in the AP.

Since, 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)

⇒ - 65 × (-2/5) = n - 1

⇒ n - 1 = 26

⇒ n = 26 + 1

⇒ n = 27

∴ Number of terms = 27.

How many terms are there in the AP 18, 15, 13, ..., - 47?