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c2 geometric sequences

With these questions I'll be required to use the n. I've noticed that sometimes the n will be n-1 or just n by itself. What decides this?

I thought when it's a geometric progression with numbers (theoretical) you use n-1 and when it's a real life example like a question on population increase, it's just n.

But i'm confused as question 2 and 4 are real life examples, but 2 uses n-1 and 4 uses n. Sorry if I haven't explained that well.

Reply 1

Prasiortle

Original post by Chrollo-Lucilfer

You are horribly confused. The first time is a, the second term is ar, the third term is ar^2, etc. In general, the nth term is ar^(n-1), since you start with a and need to multiply by r (n-1) times. In a real-life context, you have to understand what the term index represents - e.g. in a problem involving years, we could take the 1st term to be the value in "Year 0", or in "Year 1" - the context will make it clear. For example, in question 2, the first term (a) is the first/lowest gear, i.e. 40, and in question 4, the first term is the initial value of 80 whales, then the second term gives the value at the end of the first year (or the start of the second year) then the third term gives the value at the end of the second year, and so on. To refer back to what I said before, you can see that the initial value is at the start of the 1st year, or the end of the 0th year.