Question

Find the general term in simplest form for the sequence 2,1,-4,7,-10,13,-16.

There's an addition of 3 with alternating signs I think but I'm unable to find a general term.

Answer 1

suppose they were all positive:
2,1,4,7,10,13,16
that general term would be 3n-5, from the second term on
It looks like the first term is an outlier if I make that change, let's hope it works out

but we want to make the terms alternate between + and -
this can be done by (-1)^n

so the sequence can be defined as follows

term(n) = (-1)^n (3n-5)

testing:

term(1) = (-1)^1 (3 - 5) = -1(-2) = 2
term(2) = (-1)^2 (6-1) = (=1)(1) = 1
....
term(5) = (-1)^5 (15-5) = (-1)(10) = -10
term(6) = (-1)^6 (18-5) = (+1)(13 = 13

looks ok

Answer 2

Thank you