Question

Find the next number in the given sequence: $17,21,37,73,137,237,...$.

Answer 1

Calculate the next number of the given sequence:

Given sequence, $17,21,37,73,137,237,...$

The difference between the consecutive numbers are given below:

$$\begin{gathered} 21-17=4 \\ 37-21=16 \\ 73-37=36 \\ 137-73=64 \\ 237-137=100 \end{gathered}$$

It can be observed that the differences are in the form $\left(2^2\right),\left(4^2\right),\left(6^2\right),\left(8^2\right),\left({10}^2\right).....$

Thus, the difference between the next term and the last mentioned term will be ${\left(10+2\right)}^2={\left(12\right)}^2=144$.

Thus, the next term will be $237+144=381$.

Therefore, the next number of the given sequence will be $381$.