Question

What is the sum of the first twelve term of an A.P whose 1st term is 15 and the common difference is 13

Answer 1

In Arithmetic Progression:

an = a1 + ( n - 1 ) d

where

a1 = the initial term

d = the common difference of successive members

an = the nth term

In this case:

a1 = 15

d = 13

a12 = a1 + 11 d

a12 = 15 + 11 ∙ 13

a12 = 15 + 143

a12 = 158

The sum of the first n terms of arithmetic progression:

Sn = n ( a1 + an ) / 2

S12 = 12 ∙ ( a1 + a12 ) / 2

S12 = 12 ∙ ( 15 + 158 ) / 2

S12 = 12 ∙ 173 / 2

S12 = 2076 / 2

S12 = 1038

Answer 2

S12 = 12/2 (2*15 + 11*13) = 1038