SEQUENCE AND SERIES A14

The first term of an AP is 10 and the last term is 80.If the arithmetic progression consists of 30 terms, calculate the sum of all the terms.

Solution

A₁ = 10, n=30, A_n = 80

S_n = n(A₁ + A_n)

       2

S₃₀ = 30(10 + 80)

         2

S₃₀ = 15 x 90

S₃₀ = 1350

Hence the sum of all 30 terms is 1350.