Question

In a GEOMETRIC sequence, the first term is 21 andthe common ratio is 2. Find the 15th term.

Answer 1

From the question,

The geometric sequence has first term of 21 and common ratio of 2

hence

$\begin{gathered} first\text{ term, a = 21} \\ \text{common ratio, r = 2} \end{gathered}$

The general formula for nth term of a Geometric sequence is given as

$T_n=ar^{n-1}$

For the 15th term

The formula will be

$\begin{gathered} T_{15}=ar^{15-1} \\ T_{15}=ar^{14} \end{gathered}$

Applying the values of a and r

a = 21, r = 2

we have

$\begin{gathered} T_{15}=21(2)^{14} \\ T_{15}=21(16384) \\ T_{15}=344,064 \end{gathered}$

Therefore

The 15th term is 344,064