Question

The fourth term of an AP is 11. The sum of the fifth and seventh terms of the AP is 34. Find its common difference.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{a}\mathrm{be}\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{and}\mathrm{d}\mathrm{be}\mathrm{the}\mathrm{common}\mathrm{difference}. \\ \mathrm{Now},{\mathrm{a}}_4=11 \\ \Rightarrow \mathrm{a}+3\mathrm{d}=11...\left(1\right) \\ \mathrm{Also},{\mathrm{a}}_5+{\mathrm{a}}_7=34 \\ \Rightarrow \mathrm{a}+4\mathrm{d}+\mathrm{a}+6\mathrm{d}=34 \\ \Rightarrow \mathrm{a}+5\mathrm{d}=17....\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ 5\mathrm{d}-3\mathrm{d}=17-11 \\ \Rightarrow 2\mathrm{d}=6 \\ \Rightarrow \mathrm{d}=3 \end{gathered}$$