Question

If 8 times the 8th term of an APis equal to 15 times of 15th term find its 23rd term

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{a}\mathrm{be}\mathrm{the}\mathrm{first}\mathrm{term}\mathrm{and}\mathrm{d}\mathrm{be}\mathrm{the}\mathrm{common}\mathrm{difference}. \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ 8{\mathrm{a}}_8=15{\mathrm{a}}_{15} \\ 8\left(\mathrm{a}+7\mathrm{d}\right)=15\left(\mathrm{a}+14\mathrm{d}\right) \\ 8\mathrm{a}+56\mathrm{d}=15\mathrm{a}+210\mathrm{d} \\ -7\mathrm{a}=154\mathrm{d} \\ \mathrm{a}=-22\mathrm{d}...\left(\mathrm{i}\right) \\ \mathrm{Now}{\mathrm{a}}_{23}=\mathrm{a}+22\mathrm{d} \\ =-22\mathrm{d}+22\mathrm{d}\left[\mathrm{using}\left(\mathrm{i}\right)\right] \\ =0 \\ \mathrm{So},{\mathrm{a}}_{23}=0 \\ \mathrm{Note}: \\ {\mathrm{a}}_{\mathrm{n}}=\mathrm{a}+\left(\mathrm{n}-1\right)\mathrm{d} \end{gathered}$$