Problem 687

Find the sum of the first five terms of the arithmetic series: a_n =4n +7

 

Solution:-

 

Find  a₁  and  a_n  by using the explicit formula for arithmetic

sequence: a_n = a₁ + (n-1)d. The use the formula for the sum of an arithmetic series:

S_{n  =} (a₁ +a_n).

a_{1 =}  4*1 +7 =11

a₂ = 4*2+ 7 = 15

a₃ = 4*3 + 7 = 19

a₅ = 4*5  +7 = 27

d = 4

S_{n  =}  (a₁ +a_n).

=(11+27)

=95