Question

Complete the series: $23,48,99,203,413,....$

Answer 1

Find the missing term of the series by observing the pattern of the series:

Given: $23,48,99,203,413,....$

Notice the pattern:

$\begin{array}{rcl}23\times 2+2& =& 48,\\ 48\times 2+3& =& 99,\\ 99\times 2+5& =& 203,\\ 203\times 2+7& =& 413,\end{array}$

Write the general formula:

${\left(n+1\right)}^{th} \mathrm{term}=n^{th}\mathrm{term}\times 2+\mathrm{Prime}\mathrm{number}$

Notice that the numbers added $2,3,5,7$ are prime numbers. thus the next number wil be $11$.

Therefore the next term is;

$2\times 413+11=837$

Hence the complete series is $23,48,99,203,413,837$.