help needed please

Question

find the general term of the following sequences:

a) 8; 15; 22; ............

b) 8+2x; 13-2x; 18-6x; ...........

c) 8; 1; -6; .........

Answer 1

find the general term of the following sequences:

a) 8; 15; 22; ............    the common difference is 7. So the next term is 22+7 = 29

b) 8+2x; 13-2x; 18-6x; ...........      the common difference is 5 - 4x. So the next term is (18 - 6x) + (5 - 4x) = 23 - 10x

c) 8; 1; -6; .........    the common difference is -7. So the next term is -6 + (-7) = -13

Answer 2

Starting with n=1 the general term for (a) is 7n+1. But if n starts at 0, the general term is 7n+8.

(b) The common difference is 5-4x. If n starts at 0 then the general term is 8+2x+(5-4x)n; but if n starts at 1 we have to step back a term: 3+6x+(5-4x)n.

(c) The common difference is -7, so we have 8-7n if n starts from 0 and 15-7n if starts at 1.