Question

for an A.P.the first term is 10, the nth term is 40 and the sum of first n terms is 150. find the value of n and the common difference d.

Answer 1

The formula for the sum of an arithmetic sequence is :

Sn = n(a₁ + an) / 2

n = the number of terms

Sn = 150 - sum

a₁ = 10 - first term

an = 40 - last term

Doing the substitution we have :

150 = n(10 + 40)/2

150 = 50n/2

150 = 25n

n = 150/25 = 6

n = 6