Question

Find the sum of the series given in sigma notation.

Answer 1

Option b is correct 175

Explanation:

n = 7

k = 6

3k -2 ------1

put k = 6 in above eq. for finding first term

a1 = 3(6) - 2 = 18 - 2 = 16

put k = 7 in above eq. for finding first term

a2 = 3(7) - 2 = 21 - 2 = 19

a3 = 3 (8) - 2 = 24 - 2 = 22

16, 19 , 22, ... //Arithmetic series formation

a1 = 16 , a2 = 19

d = a2 - a1 = 19 - 16 = 3 //Difference of first two terms

Using sum forumula for arithmetic series

sum =
`(n)/(2)(2a1 + (n-1)d)`

=
`(7)/(2)(2a1 + (7-1)d)`

=
`(7)/(2)(2(16) + (6)3)`

=
`(7)/(2)(32 + 18)`

=
`(7)/(2)(50)`

= 7 * 25

= 175