Question

15 POINTS**
Write an explicit formula an, the nth term of the sequence 27,-3,-33,-63

Answer 1

The nth term is 27 - 30(n-1) or can be simplified to 57 - 30n.

Explanation:

This is an arithmetic sequence (ie. each term equals the previous term with a constant value added (or subtracted from it)

T1 = 27

T2 = -3 = T1 - 30 = 27 - 30

T3 = -33 = T2 -30 = 27 -30 - 30=27-30X(2)

T4= -63 = T3 - 30 =27-30X(2)-30=27-30X(3)

In general, the nth term of this sequence:

S(n) = 27 - 30X(n-1)