Question

In the following AP, find the missing term
7, *, *, 6

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{a}\mathrm{be}\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{and}\mathrm{d}\mathrm{be}\mathrm{the}\mathrm{common}\mathrm{difference}. \\ \mathrm{So},\mathrm{a}=7 \\ \mathrm{and}{\mathrm{a}}_4=6 \\ \mathrm{We}\mathrm{know}\mathrm{that}{\mathrm{a}}_{\mathrm{n}}=\mathrm{a}+\left(\mathrm{n}-1\right)\mathrm{d} \\ \mathrm{Put}\mathrm{n}=4,\mathrm{we}\mathrm{get} \\ {\mathrm{a}}_4=\mathrm{a}+\left(4-1\right)\mathrm{d} \\ \Rightarrow 6=7+\left(4-1\right)\mathrm{d} \\ \Rightarrow 6-7=3\mathrm{d} \\ \Rightarrow -1=3\mathrm{d} \\ \Rightarrow \mathrm{d}=\frac{-1}{3} \\ \mathrm{So},{\mathrm{a}}_2=\mathrm{a}+\mathrm{d} \\ =7+\left(\frac{-1}{3}\right) \\ =7-\frac{1}{3} \\ =\frac{20}{3} \\ \mathrm{and}{\mathrm{a}}_3=\mathrm{a}+2\mathrm{d} \\ =7+2\left(\frac{-1}{3}\right) \\ =7-\frac{2}{3} \\ =\frac{19}{3} \\ \mathrm{So}\mathrm{missing}\mathrm{terms}\mathrm{are}: \\ {\mathrm{a}}_2=\frac{20}{3}\mathrm{and}{\mathrm{a}}_3=\frac{19}{3} \end{gathered}$$