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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

2 Answers

6 votes

Answer:

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)

User Aktivb
by
6.8k points
3 votes

Answer:

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),...

User InvalidSyntax
by
7.0k points