Question

the 7 th term of an ap is -4 and its 18 th term is-16 then find its ap.

Answer 1

$$\begin{gathered} \mathrm{Hi}, \\ \mathrm{Let}\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{is}\mathrm{a}\mathrm{and}\mathrm{common}\mathrm{difference}\mathrm{is}\mathrm{d}\mathrm{so} \\ \mathrm{a}+6\mathrm{d}=-4 \\ \mathrm{and} \\ \mathrm{a}+17\mathrm{d}=-16 \\ \mathrm{Subtracting},\mathrm{we}\mathrm{get} \\ 11\mathrm{d}=-12 \\ \mathrm{d}=\frac{-12}{11} \\ \mathrm{and}\mathrm{hence}\mathrm{a}=-4-6\mathrm{d}=-4+\frac{12}{11}=\frac{-32}{11} \\ \mathrm{So}\mathrm{AP}\mathrm{is}\frac{-32}{11},\frac{-32}{11}+\frac{-12}{11},\frac{-32}{11}+\frac{-2\times 12}{11},\frac{-32}{11}+\frac{-3\times 12}{11},.... \\ \mathrm{Similpify}\mathrm{this}\mathrm{to}\mathrm{get}\mathrm{the}\mathrm{answer}. \\ \mathrm{Regards} \end{gathered}$$