Question

The eighth term of the geometric sequence -3, 9, -27, 81, .... is
A. -6.561
B. -2.187
C. 2.187
D. 6.561
(please, help me on this ^^)

Answer 1

$\small{\orange{ \boxed{ \boxed{ \begin{array}{cc}\hookrightarrow \sf \: \: given \: the \: G.P \: series \: : \\ \\ \sf \: - 3,9, - 27,81. \: . \: . \: \\ \\ \blue{ \underline{\sf \: we \: have \: to \: find : }} \\ \\ \hookrightarrow \sf \: {8}^{th} \: term \: of \: the \: G.P \: series = T_8\\ \\ \\ \red{ \underline{ \sf \: solution :}} \\ \\ \hookrightarrow \: \sf \: first \: term \: of \: the \: G.P \: series, \: a = - 3 \\ \\ \hookrightarrow \sf \:common \: ratio \: of \: the \: G.P \: series ,\: r = \frac{9}{ - 3} = - 3 \\ \\ \\ \pink{ \underline{ \sf \: we \: know \: that : }} \\ \\ \hookrightarrow \: \sf \: general \: term \: of \:G.P \: series \: \: T_n= a {r}^{n - 1} \\ \\ \\ \bf \: now \: according \: to \: the \: question \: \\ \\ \sf \: T_8 = - 3 \times {( - 3)}^{8 - 1} \\ \\ = - 3 \times {( - 3)}^{7} \\ \\ = 3 \times {3}^{7} \\ \\ = {3}^{8} \\ \\ = 6561 \\ \\ \blue{ \boxed{\therefore \sf \: {8}^{th} \: term \: of \: the \: series \: is = 6561}} \\ \\ \end{array}}}}}$