Question

in a GP the fourth term is 48 and the eighth term is 768. find the tenth term​

Answer 1

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Given ,

$\star \: \: \sf 4th \: term \: of \: GP = 48 \\ \to \sf a {r}^{3} = 48 \: ------- \:eq(i) \\ \\ \star \: \: \sf</p><p>8th \: term \: of \: GP = 768 \\ \sf \to a {r}^{7} = 768\: ------ \:eq(ii)$

Dividing equation (ii) and (i) , we get ,

$\to \sf \frac{a {r}^{7} }{a {r}^{3} }= \frac{768}{48} </p><p> \\ \\ \to \sf</p><p> {r}^{4} = 16</p><p> \\ \\ \to \sf</p><p> r = 2$

Putting r = 2 in eq (i) , we get ,

$\to \sf a {r}^{3} = 48 \\ \\ </p><p> \to \sf </p><p>a \times {(2)}^{3} = 48</p><p></p><p> \\ \\ \to \sf a \times 8 = 48</p><p></p><p> \\ \\ \to \sf a = 6$

Now ,

$\to \sf 10th \: term = a {r}^{9} \\ \\ \to \sf 10th \: term = 6 \times {(2)}^{9} \\ \\ \to \sf</p><p>10th \: term = 6 × 512</p><p> \\ \\ \to \sf </p><p>10th \: term = 3072$

Hence , the required number is 3072