Question

In an AP, the first term is –4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

Answer 1

Suppose there are n terms in the AP.

Here, a = 4, l = 29 and S_n = 150 

S_n = 150

⇒ `n/2 (-4 + 29) = 150`   ...`[S_n = n/2 (a + l)]`

⇒ `n = (150 xx 2)/25`

⇒ n = 12

Thus, the AP contains 12 terms.

Let d be the common difference of the AP.

∴ a₁₂ = 29

⇒ –4 + (12 – 1) × d = 29   ...[a_n = a + (n – 1)d] 

⇒ 11d = 29 + 4

⇒ 11d = 33

⇒ `d = 33/11`

⇒ d = 3 

Hence, the common difference of the AP is 3.