Question

In a GP if T3 = 18 and T6 = 486 Find:- T10

Answer 1

Step-by-step explanation:

$T_3 = a {r}^{2} = 18....(1) \\ T_6 = a {r}^{5} = 486...(2) \\ dividing \: equation \: (2) \: by \: (1) \\ \frac{a {r}^{5} }{a {r}^{2} } = \frac{486}{18} \\ {r}^{3} = 27 \\ {r}^{3} = {3}^{3} \\ r = 3 \\ \implies \: a {3}^{2} = 18 \\ \implies \: a \times 9 = 18 \\ \implies \: a = \frac{18}{9} = 2 \\ now \\ T_{10} = a {r}^{9} = 2 \times {3}^{9} \\ T_{10} = 2 \times 19683 \\ T_{10} = 39366$