Question

Find the 12th term of G.P whose 8th term is 192 and the common ratio is 2

Answer 1

nth term = ar^n-1

12th term = ar^11

8th term = ar^7

192= a*2^7

a= 192/2^7

=3/2

12th term = 3/2*2^11

= 3072

Answer 2

$\underline{\underline{\mathfrak{\Large{Solution : }}}} \\ \\ \\ \underline {\sf {Given,}} \\ \\ \\ \sf\: Common \: ratio\: r = 2 \\ \\ \\ \underline {\sf {To \: Find :}} \\ \\ \\ \sf\: 12th \: term \: of \: G.P \\ \\ \\ \underline {\sf {Procedure :}} \\ \\ \\ \sf\: 8th \: term \: = 192 \\ \\ \\ \sf\implies\: ar^{8-1} = 192 \\ \\ \\ \sf\implies\: a × 2^7 = 192 \\ \\ \\ \large {\sf {\boxed { a = \dfrac {192}{128} = \dfrac {3}{2}}}} \\ \\ \\ \sf\: 12th\: term\: of\: G.P = ar^{12-1} = ar^{11} \\ \\ \\ \sf\implies\dfrac {3}{2} × 2^{11} = 3072 \\ \\ \\ \sf\: Hence\:12th\: term\: of\: G.P \: is \: = 3072$