# What is the nth term for these sequences?

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Ok so the formula for finding the nth term of a sequence is: nth term = dn + (a - d) where d= the common difference (i.e. the gap between each number of the sequence) and where a is the first term

10 May 2011

which simplifies to n=6n +3

10 May 2011

so the nth term is n=6n + (9-6)

10 May 2011

So for the first set of sequences the common difference is +6 (as 15-9 = 6 and 21-15 = 6) and the first term is 9

10 May 2011

For the next sequence the common difference is 5 and the first term is 2 so going back to our original formula of nth term = dn + (a-d) we just substitute in the 5 and the 2 for the d and the a:

10 May 2011

n= 5n - 3

10 May 2011

n= 5n + (2-5)

10 May 2011

for the final one, the common difference = -8 and the first term =20 so we get:

10 May 2011

which gives us n = -8n +28 ( because a minus and a minus = a plus)

10 May 2011

n= -8n + (20 - -8)

10 May 2011

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