Question

(ii) Which term of the AP: 21, 18, 15, . . . is – 81?​

Answer 1

your answer is provided in the above attachment.

Answer 2

$\texttt{first term, a = 21}$

$\texttt{common difference, d = 18 - 21 = -3}$

$\mathtt{T_{n} = -81}$

$\texttt{n = ?}$

$\mathtt{ \;\;\;\;\;\;\; T_{n} = a+(n-1)d}$

$\implies \mathtt{ -81 = 21 + (n-1)×(-3)}$

$\implies \mathtt{-81-21 = -3(n-1)}$

$\implies \mathtt{-\!\!\!/102 = -\!\!\!/3(n-1)}$

$\implies \mathtt{3(n-1) = 102}$

$\implies \mathtt{(n-1) = \large \frac{102}{3}}$

$\implies \mathtt{n-1 = 34}$

$\implies \mathtt{n = 34+1}$

$\implies \mathtt{n = 35}$

$\therefore \mathtt{The \; 35^{th} \; term \; of \; the \; AP \; is \; -81}$