Chapter 8, Problem 10CUR

To determine

To Find : The next two numbers in the given sequence.

Answer to Problem 10CUR

The required terms are 92 and 141.

Explanation of Solution

Given information:

The series $1,2,6,15,31,56,\mathrm{......}$

Calculate the difference between nearest number.

  $\begin{array}{l}\begin{array}{l}2–1=1\hfill \\ 6–2=4\hfill \\ 15–6=9\hfill \\ 31–15=16\hfill \end{array}\\ 56–31=25\end{array}$

The difference of the consecutive numbers is square of consecutive natural number.

Therefore, the next two numbers of series can be calculated as,

  $\begin{array}{l}56+36=92\hfill \\ 92+49=141\hfill \end{array}$

Therefore, the required terms are 92 and 141.