Question

Find the next term of the series: $1728,2744,4096,5832,8000,10648,?$.

• A. $2167$
• B. $13824$
• C. $15625$
• D. $9261$
• E. $17576$

Answer 1

The correct option is B

$13824$

Explanation for correct option:

Given series, $1728,2744,4096,5832,8000,10648,?$.

Given series follows a specific pattern. That is,

$$\begin{gathered} {12}^3=1728 \\ {14}^3=2744 \\ {16}^3=4096 \\ {18}^3=5832 \\ {20}^3=8000 \\ {22}^3=10648 \end{gathered}$$

Thus, the general term of the series can be given by, $t_n={\left(2n+10\right)}^3$.

Thus, the next term of the series can be determined by,

$\begin{array}{rcl}{t}_7& =& {\left[\left(2\times 7\right)+10\right]}^3\\ & =& {\left(14+10\right)}^3\\ & =& {24}^3\\ & =& 13824\end{array}$.

Therefore, the next term of the given series is $13824$.