Question: Find the Value of Term 4

Comment on Find the Value of Term 4

Brent, with a question like this, how does one save time by not trying the first method which leads to an unknown variable
Thanks
gmat-admin's picture

I think that it would only take a few seconds before you realize that this approach leads nowhere.

That said, the question tells us that the value of term_n depends on the values of term_n-2 and term_n-1. In other words, we need to know the two terms BEFORE term_n in order to calculate term_n.

In other words, this sequence is a recursive (see previous video lesson), which means you can't just plug the require n-value into the formula.

Does that help?

Hi Brent, please may you explain the significance of n≥3. Initially I thought this meant that the sequence only applies when the term plugged in is equal to or more than 3. I understand that this is incorrect because we used the sequence to solve for x2. Thank you
gmat-admin's picture

Great question!

Notice that the value of any term depends on the values of the TWO terms before it.

For example, term7 = 2(term5) - 4(term6)
Likewise, term10 = 2(term8) - 4(term9)
And term13 = 2(term11) - 4(term12)

This also means that term2 = 2(term1) - 4(term0)
Hmm, the sequence starts with term1. So, there is no term0.

Since there is no term0, it doesn't make sense to use the formula (for finding terms) to find term2 and term1.
So, the proviso (n ≥ 3) tells us that the formula only applies to term3, term4, term5, etc.

Does that help?

Cheers,
Brent

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