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Question from Joanne, a student:

Find the first five terms of the sequences with the nth term given as follows.
n^2+3n

Joanne,

The letter n indicates which term you are looking at

when n = 1 you have the first term,
when n = 2 you have the second term,
when n = 3 you have the third term,
and so on.

So to find the first term let n = 1 and you get

n2 + 3n = 12 + 3 × 1 = 1 + 3 = 4.

To find the second term let n = 2 and you get

n2 + 3n = 22 + 3 × 2 .

To find the second term let n = 3, and so on.

You need to read carefully because sometime the sequence starts with n = 0 rather than n = 1. So if your sequence is n2 + 3n for n = 0, 1, 2, ... the first term would be

n2 + 3n = 02 + 3 × 0 = 0 + 0 = 0,

and the second term would be

n2 + 3n = 12 + 3 × 1 = 1 + 3 = 4.

I hope this helps,
Penny

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