Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.)
{-9,6,-4,8/3,-16/9}

Answer 1

Answer:

-9(-2/3)^{n-1}

Step-by-step explanation:

Given the sequence

-9,6,-4,8/3,-16/9

The sequence is a geometric progression. The nth term of a geometric progression is expressed as;

Tn = ar^{n-1}

a is the first term = -9

r is the common ratio = 6/-9 = -4/6 = -2/3

n is the number of terms

Substitute the given parameters into the formula;

Tn = -9(-2/3)^n-1

Hence the formula for the general term an of the sequence is  -9(-2/3)^{n-1}