Question

Based on the pattern, what are the next two terms of the sequence? 9,9/5, 9/25 , 9/125 , 9/625 . . .

A. 9/3125 , 9/3130

B. 9/630, 9/3130

C. 9/3125, 9/15625

D. 9/630 , 9/635

Answer 1

Option C.
`(9)/(3125) and (9)/(15625)`

Explanation:

The given sequence is
`9, (9)/(5), (9)/(5^(2) ), (9)/(5^(3)), (9)/(5^(4)).........`

This sequence is the geometric sequence of which first term is 9,

and common difference
`r=((9)/(5) )/(9)=(9)/((5)(9))=(1)/(5)`

As we know explicit formula of a geometric sequence is

`T_(n)=ar^(n-1)`

where n is the number of term.

We have to get 6th and 7th term of the sequence.

`T_(6)=9.((1)/(5))^(6-1)=(9)/(5^(5) )`

and
`T_(7)=9.((1)/(5))^(7-1)=9.((1)/(5))^(6)`

Therefore answer will be next two terms are
`(9)/(3125) and (9)/(15625)`

Answer 2

The answer is the option C

`(9)/(3,125), (9)/(15,625)`

Explanation:

we have

`9, (9)/(5),(9)/(25),(9)/(125),(9)/(625),...`

Rewrite the sequence

`(9)/(5^(0)), (9)/(5^(1)),(9)/(5^(2)),(9)/(5^(3)),(9)/(5^(4)),...`

therefore

The next two terms of the sequence are

`(9)/(5^(5)), (9)/(5^(6)),...`

`(9)/(3,125), (9)/(15,625),...`