If $8^{ ext {th }}$ term of a GP is 192 and Common ratio is 2 , then $\mathrm{t}_{12}=$ $\_\_\_\_$

Question

If $8^{	ext {th }}$ term of a GP is 192 and Common ratio is 2 , then $\mathrm{t}_{12}=$ $\_\_\_\_$

Professor PC Thomas Classes · Answer

$t_8 = a r^7 = 192 \implies a(2^7) = 192 \implies 128a = 192 \implies a = 1.5$. $t_{12} = a r^{11} = 1.5(2^{11}) = 1.5(2048) = 3072$.