Question

Find the sum of the first k terms of a series whose n th term is 2an+b The n th term of the AP is given by 2an+b

Answer 1

a1=2a+b
a2 =4a+b
a3=6a+b
Common difference = d=( 4a + b ) - ( 2a + b ) = 2a

Therefore, sum of first k terms =k/2[(2a+(k-1)d]= k/2[(2(2a+b)+(k-1)2a]= k/2 x 2
(2a+b+k-a)=k(a+b+ak)