FIND THE NTH TERM IN THE

SEQUENCE 1,6,13,22,33

The differences are 5,7,9,11..so, again, we know that the pattern is n^2.

The second differences are 2, a constant.

Next, we have to find the link. We notice that the first difference is 5 not 3. This

means that the series of square numbers we use start at 4 and NOT 1.

It follows that to obtain 4,9,16,25... from the original sequence simply add 3 to

each term of the sequence.

So, to get from the square numbers to the sequence 1,6,13,22,33... we have to

use (n+1)^2, since the sequence is based on 4,9,16...

The final step in finding the rule is to take away the three, which give the nth

term as:

(n+1)^2-3…read more

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