Question

For a G.P. sum of first 3 terms is 125
and sum of next 3 terms is 27,
find the value of r.​

Answer 1

Answer:

$let \: the \: first \: term \: of \: g .p. \: is \: a \: and \: common \: ratio \: is \: r. \\ then \: according \: to \: the \: question \\the \: sum \: of \: first \: three \: = 1 25 \\ a + ar + a {r}^{2} = 125 \\ a(1 + r + {r}^{2} ) = 125..............(1) \\ the \: sum \: of \: next \: three \: term \: = 27 \\ a {r}^{3} + a {r}^{4} + a {r}^{5} = 27 \\ a {r}^{3} (1 + r + {r}^{2} ) \: = 27.............(2) \\ divide \: equation \: (2) \: from \: (1) \\ \frac{a {r}^{3} (1 + r + {r}^{2} )}{a(1 + r + {r}^{2}) } = \frac{27}{125} \\ {r}^{3} = \frac{27}{125} \\ r = \frac{3}{5}$

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