# What is the nth term for these sequences?

9, 15, 21, 27, 33 nth term=

2, 7, 12, 17, 22 nth term=

20,12, 4, -4, -12 nth term=

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
chloe
10 May 2011
which simplifies to n=6n +3
chloe
10 May 2011
so the nth term is n=6n + (9-6)
chloe
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
chloe
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:
chloe
10 May 2011
n= 5n - 3
chloe
10 May 2011
n= 5n + (2-5)
chloe
10 May 2011
for the final one, the common difference = -8 and the first term =20 so we get:
chloe
10 May 2011
which gives us n = -8n +28 ( because a minus and a minus = a plus)
chloe
10 May 2011
n= -8n + (20 - -8)
chloe
10 May 2011 