Question

THE SUM OF FIRST 20 TERMS OF A G.P. IS 244 TIMES THE SUM OF ITS FIRST 10 TERMS. the comman ratio is?​

Answer 1

Answer:

A/Q

$s_{20} =244 \times s_{10}$

$\frac{a( {r}^{20} - 1)}{r - 1} = 244 \times \frac{a( {r}^{10} - 1) }{r - 1}$

${r}^{20} - 1 = 244 {r}^{10} - 244$

$let \: {r}^{10} = x$

${x}^{2} - 1 = 244x - 244$

${x}^{2} - 244x + 243 = 0$

${x}^{2} - 243x - x + 243 = 0$

$x(x - 243) - 1(x - 243) = 0$

$x = 1 \: \: or \: 243$

but x=1 not taken because r become 1.

so x = 243 i.e

${r}^{10} = 243 = ( \sqrt{3} ) {}^{10}$

$r = \sqrt{3} \: \: \: ans.$