# Calculus 2 - Series

I am so confused on how to do series problems...especially these. How can you tell the pattern and determining the formula for them?

26) Write the first five terms of the sequence {an} whose nth term is given.

an = (n + 3)/(2n − 1)

a1 = ?
a2 = ?
a3 = ?
a4 = ?
a5 = ?

27) Find an expression for the nth term of the sequence. (Assume that the pattern continues.)

{3/4, 4/9, 5/16, 6/25, 7/36, ...}

an = ??

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1. an = (n + 3)/(2n − 1)
well, just start plugging in values for n:
a1 = (1+3)/(2*1-1) = 4/1 = 4
a2 = (2+3)/(2*2-1) = 5/3
and so on ...

Look at the numerators:
3,4,5,... = n+2
and the denominators:
4,9,16,... (n+1)^2
So, an = (n+2)/(n+1)^2

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2. Ahh, for the first problem, I wasn't sure if I was supposed to plug in numbers (1-5) or if there was a particular number I was to plug in rather than randomly, but now realizing that it's between a1-a5 with the numbers accordingly.

And for the second problem, I was trying to find a GCF, but it didn't go so well. But I understand it a bit more now. Thank you so much Steve. :)

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3. yeah - sometimes it's possible to overthink this stuff. It just takes practice, like anything else.

Good judgment comes from experience.

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