Question

Write an explicit formula for the geometric sequence below and use it to find the 9th term.

256, 64, 16, 4, . . .

Answer 1

The explicit formula is;

Tn = 256(1/4)^(n-1)

The 9th term is;

256/65536

Explanation:

Mathematically, we have the nth term of a geometric sequence as;

Tn = ar^(n-1)

a is the first term = 256

r is the common ratio = 64/256 = 16/64 = 4/16 = 1/4

So, for the 9th term, we have

T9 = 256(1/4)^(9-1) = 256/65536

The explicit formula is;

Tn = 256(1/4)^(n-1)