Question

The n^th term of a sequence is given by a_n = 2n + 7. Show that it is an A.P. Also, find its 7th term.

Answer 1

$$\begin{gathered} a_n=2n+7 \\ \therefore a_1=2\times 1+7=9 \\ {a}_2=2\times 2+7=11 \\ {a}_3=2\times 3+7=13 \\ {a}_4=2\times 4+7=15 \\ \mathrm{and}\mathrm{so}\mathrm{on} \\ \mathrm{So},\mathrm{common}\mathrm{difference}\left(d\right)=11-9=2 \\ \mathrm{Thus},\mathrm{the}\mathrm{above}\mathrm{sequence}\mathrm{is}\mathrm{an}A.P.\mathrm{with}\mathrm{the}\mathrm{common}\mathrm{difference}\mathrm{as}2 \\ {a}_7=2\times 7+7=21 \end{gathered}$$