# Lesson: Recursive Definitions of Terms

## Comment on Recursive Definitions of Terms

### https://gmatclub.com/forum/in

https://gmatclub.com/forum/in-a-certain-sequence-term1-64-and-for-all-267905.html

If we start from back
t11/t8 = t10*2^11
= t9*2^10*2^11
= t8*2^10*2^11*2^9
= t7*2^30*2^8/t7*2^8
= 2^30

Nice!

### What is the best way to

What is the best way to figure out if you are dealing with a recursive sequence?

### A quick/easy way to identify

A quick/easy way to identify a recursive sequence is to try finding the value of a random term.

For example, it you try to find the value of term_10, and you discover that, in order to find term_10, you must first find the value of term_9, then you're dealing with a recursive sequence.

Does that help?

Cheers,
Brent

### Hi Brent,

Hi Brent,

Doubt regarding this question: <https://gmatclub.com/forum/in-the-sequence-s-of-numbers-each-term-after-the-first-two-terms-is-167947.html>

It is clear that Statement 1 is SUFF, however I also find Statement 2 SUFF, since I could rephrase the target question transforming S5 to an equation involving S1. Hence, Statement2 is : whateverquestioninvolvingS1 = 21.

May you help me? Cheers.

Sorry, I'm not sure what you mean by "rephrase the target question transforming S5 to an equation involving S1.Hence, Statement2 is : whateverquestioninvolvingS1 = 21." San you please elaborate on this approach?
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In the meantime....

TARGET QUESTION: What is the value of term5?

Statement 2 tells us that term6 + term7 = 21.

To show that Statement 2 is not sufficient, consider these two conflicting cases:

CASE i: term6 = 10 and term7 = 11
Since we know that term7 = term5 + term6, we can write: 11 = term5 + 10
So, in this case, term5 = 1

CASE ii: term6 = 9 and term7 = 12
Since we know that term7 = term5 + term6, we can write: 12 = term5 + 9
So, in this case, term5 = 3

Since we can't answer the target question with certainty, statement 2 is not sufficient.

Does that help?