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 = (150xx 2) / 25 = 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 = 33

⇒ d= 3 

Hence, the common difference of the AP is 3.