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## Comment on

Introduction to Sequences## Each term in sequence S is

Each term in sequence S is determined by multiplying the prior term by 2 and dividing that product by 3. What is the 100th term of the sequence S?

(1) The sum of the first 2 terms is 15

(2) The first term of the sequence is 9

## Hi Rajkumar,

Hi Rajkumar,

I just posted a solution to that question here: https://gmatclub.com/forum/each-term-in-sequence-s-is-determined-by-mult...

Cheers,

Brent

## Sir, but in statement 2,

If we multiply the first term by 2/3 we are getting the second term as 6, and next terms 4,8/3......etc.Here the common difference varies.Hence how it is possible to find 100th term?

## Here's how:

Here's how:

term1 = 9

term2 = (9)(2/3) = 6

term3 = (9)(2/3)(2/3) = 4

term4 = (9)(2/3)(2/3)(2/3) = 8/3

term5 = (9)(2/3)(2/3)(2/3)(2/3) = 16/9

.

.

.

If you recognize that we can keep doing this indefinitely, then you can see that we COULD determine the value of term100

We might also see the pattern and recognize that term100 = (9)(2/3)^99

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