Question

Find the next term in the series 2, 3, 8, 63.

Answer 1

We treat the given problem as a reasoning problem where we observe the problem and try to find the condition. In this case we find the terms by subtracting 1 from the square of its previous number. We follow the process to find the solution.

Complete step by step answer:
This given series is more of a reasoning problem than core mathematics.
We first need to visualise the give number where we have $2$
\Rightarrow 3=4-1={{2}^{2}}-1 \\\ \Rightarrow 8=9-1={{3}^{2}}-1 \\\ \Rightarrow 63=64-1={{8}^{2}}-1 \\\
So, we can see that we are finding a number by subtracting 1 from the square of its previous number.This is not a regular A.P. or G.P. or A.G.P series.Now we get the next term by taking ${{63}^{2}}-1=3969-1=3968$.

Therefore, the next term in the series 2, 3, 8, 63 is 3968.

Note: The condition will be applied for all the numbers except the starting number. The starting number cannot be found from the condition as it doesn’t follow it. To solve these types of problems we need to apply observation more than calculation.