Question

In an A.P.,the first term is -4,the last term is29 and the sum of all its term is 150.find its common difference​

Answer 1

Answer :

Let the common difference be d and the number of terms be n.

Here, a = -4 and Tn = 29

Sn = 120

Sn = n/2 ( a + Tn )

150 = n/2 ( -4 + 29 )

150 = n/2 × 25

(150 × 2)/25 = n

300/25 = n

12 = n

Number of terms = 12

Tn = T6 = 29

Tn = a + (n - 1)d

29 = -4 + (12 - 1) × d

33 = 11 d

3 = d

Hence, The common difference = d = 3.

Hope it helps!