Question

if T3: 9 and T5: 81 find geometric progression​

Answer 1

For a Geometric Progression;

$t_{3} = 9 \\</p><p>t_{5} = 81 \\</p><p>\: \: \: \: \: \frac{t_{5}}{t_{3}} = {81}{9} \\</p><p>\frac{a{r}^{4}}{a{r}^{2}} = 9$ ... $t_{n} = a{r}^{n - 1}$

$</p><p>{r}^{2} = 9 \\</p><p>r = ±3$

$t_{3} = 9 \\</p><p>a{r}^{2} = 9 \\</p><p>a{(±3)}^{2} = 9 \\</p><p>a(9) = 9 \\</p><p>a = 1$

when r = 3, the G.P. becomes 1, 3, 9, 27, 81, ...

when r = -3, the G.P. becomes 1, -3, 9, -27, 81, ...

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