The sum of 20 terms of a series of which every even term is 2 times the term before it, every odd term is 3 times the term before it, the first term being unity is a. `(2/7)(6^(10)-1)` b. `(3/7)(6^(10)-1)` c.`(3/5)(6^(10)-1)` d. none of these

Options

A. `(2/7)(6^10-1)`
B. `(3/7)(6^10-1)`
C. `(3/5)(6^(10)-1)`
D. none of these

Answer

C

Explanation

The series is
`1+2+2xx3+2^(2)xx3+2^(2)xx3^(2)+2^(3)xx3^(2)+….` to 20 terms
`=(1+2xx3+2^(2)xx3^(2)+…` to 10 terms)
`=(1(2^(103^(10)-1)))/(6-1)+(2(2^(10)3^(10)-1))/(6-1)=(3/5)(6^(10)-1)`