Question

Complete the series $4,5,12,39,160,.....$

Answer 1

Observe the pattern and complete the series.

Observe the successive numbers in the series and obtain the general form of the sequence:

from,$4,5,12,39,160,.....$

$$\begin{gathered} 4\times 1+1=5 \\ 5\times 2+2=12 \\ 12\times 3+3=39 \\ 39\times 4+4=160 \end{gathered}$$

thus the general form of the sequence obtained is${(n+1)}^{th}\mathrm{term}=n^{th}\mathrm{term}\times n\mathit{+}n$

thus,

$\mathit{\Rightarrow }\mathit{}{(n+1)}^{th}\mathrm{term}=\left(n\right)$

and

$$\begin{gathered} \Rightarrow 7^{th}\mathrm{term}=(6^{th}\mathrm{term}\times 6)+6 \\ \Rightarrow 7^{th}\mathrm{term}=805\times 6+6 \\ \Rightarrow 7^{th}\mathrm{term}=4836 \end{gathered}$$

Therefore, the next terms in the series are $805,4836,.....$

Hence, the complete series is $4,5,12,39,160,805,4836,......$