Question

Complete the recursive formula of the geometric sequence -0.56\,,-5.6\,,-56\,,-560,...−0.56,−5.6,−56,−560,...Minus, 0, point, 56, comma, minus, 5, point, 6, comma, minus, 56, comma, minus, 560, comma, point, point, point. C(1)=c(1)=c, left parenthesis, 1, right parenthesis, equals c(n)=c(n-1)\cdotc(n)=c(n−1)⋅c, left parenthesis, n, right parenthesis, equals, c, left parenthesis, n, minus, 1, right parenthesis, dot

Answer 1

The recursive formula is:

Cn = 10C(n-1)

Explanation:

Given the geometric sequence.

-0.56, -5.6, -56, -560, ...

The common ratio is

-5.6/-0.56 = -56/-5.6 = -560/-56 = ... = 10

The recursive formula is easily

Cn = C(n-1) × 10

That is a number is ten times the preceding number.