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 Question from Rachel, a parent: I am trying to help my son get ready for our Aims test and I am not much help. The sequence is 2,5,10,17 The question is which equation represents the rule for finding the nth term for this sequence a. $a_n=n + 1$ b. $a_n=2n^2$ c. $a_n=n^2+1$ d. $a_n=2n+1$

Hi Rachel,

With multiple choice questions, if you don't see the correct choice immediately then try to eliminate some of the options. For example in this problem you have four terms of a sequence, 2, 5, 10 and 17 and hence $n = 1, 2, 3, \mbox{ and } 4.$

Look at option a.

The expression given in option a. is $n + 1$ so the terms would be

1 + 1 = 2
2 + 1 = 3

and already this doesn't work as the second term in your sequence is 5.

Next try option b.

The expression given is $2 n^2$ so each term is 2 times something and hence the terms are all even. The second term in your sequence is 5 which is not even so option b. is not the correct choice.

Now option c.

The expression is $n^2 + 1$ so each term in this sequence is 1 more than a square. Try this with your sequence.

$2 = 1 + 1 = 1^2 + 1$
$5 = 4 + 1 = 2^2 + 1$
$10 = 9 + 1 = 3^2 + 1$
$17 = 16 + 1 = 4^2 + 1$

so this works and the correct option is c.

There is no need to go through the options in order as I did. For example you might have seen immediately that d. is not the correct option. When $n = 1$ the expression for d. gives $2n + 1 = 3$ and the first term of your sequence is 2.

I hope this helps,
Penny

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