Question

The first term of a geometric sequence is 216 and common ratio is 1/3 .Write the first five terms of the sequence.

Answer 1

SOLUTION

The question is a geometric sequence.

The first term (a) = 216

The common ratio = r

The second term is

$ar\text{ = 216 x }\frac{1}{3}\text{ = 72}$

The third term is

$ar^2=216\text{ x }\frac{1}{3^2}\text{ = }\frac{216}{9}\text{ = 24}$

The fourth term is

$ar^3\text{ = 216 x }\frac{1}{3^3}\text{ = }\frac{216}{27}\text{ = 8}$

The fifth term is

$ar^4\text{ = 216 x }\frac{1}{3^4\text{ }}=\text{ }\frac{216}{81}\text{ = }2.67$

Thus, the first five terms of the geometric sequence are 216, 72, 24, 8 and 2.67.