Question

Complete the pattern: $8,3,-2,-{7_{,\_\_,\_\_}}_{.}$

Answer 1

Find the missing terms by observing the pattern of the series.

Given series is: $8,3,-2,-{7_{,\_\_,\_\_}}_{.}$

It is observed that the series is in A.P.

Arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant.

Here,$8$ is the first term

Find the common difference $\mathrm{say}\text{'}d\text{'}$:

$$\begin{gathered} \Rightarrow d=2^{nd}\mathrm{term}-1^{st}\mathrm{term} \\ \Rightarrow \mathrm{d}=3-8 \\ \Rightarrow d=-5 \end{gathered}$$

We also know that,

In A.P.,$n^{th}\mathrm{term}={(n-1)}^{th}\mathrm{term}+d$

Thus,

$$\begin{gathered} \Rightarrow 5^{th}\mathrm{term}=4^{th}\mathrm{term}+d \\ \Rightarrow 5^{th}\mathrm{term}=-7-5 \\ \Rightarrow 5^{th}\mathrm{term}=-12 \end{gathered}$$

and

$$\begin{gathered} \Rightarrow 6^{th}\mathrm{term}=5^{th}\mathrm{term}+d \\ \Rightarrow 6^{th}\mathrm{term}=-12-5 \\ \Rightarrow 6^{th}\mathrm{term}=-17 \end{gathered}$$

Hence the complete the pattern is $8,3,-2,-7,\underline{-12,-17.}$