Question

The n th term of a sequence is an=2n+7 show that it is in ap. Also find its 8 th term

Answer 1

Step-by-step explanation:

$Given: \: a_n=2n+7 \: .....(1) \\ substitute \: n = n + 1 \\ \: a_{n + 1}=2(n + 1)+7......(2) \\ subtrcting \: (1) \: from \: (2) \\ a_{n + 1} - a_n=2(n + 1)+7 - (2n+7) \\ = 2n + 2 + 7 - 2n - 7 \\ = 2 \\ \because \: difference \: between \: two \: terms \: \\ of \: the \: given \: sequence \: is \: a \: constnt \\ \therefore \: given \: sequence \: is \: AP.\\a_8=2\times 8+7 \\a_8=16+7\\a_8=23$