Question

Find the gp whose 4th term is 24 and 7th term is 192 also find sum of first 10 terms

Answer 1

Let first term be a and common ratio be r
$t4 = a \times {r}^{3} = 24 - - - (1) \\ t7 = a \times {r}^{6} = 192 - - - (2) \\ \frac{(2)}{(1)} \: gives \\ {r}^{3} = \frac{192}{24} = 8 \\ r = 2 \\ from \: \: (1) \: a = \frac{24}{ {2}^{3} } = 3$

Thus GP is 3, 6, 12,....

$s10 = \frac{a( {r}^{10 } - 1)}{r - 1} \\ = \frac{3 \times ( {2}^{10 } - 1)}{2 - 1} = 3069$

Answer 2

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