Let A1, A2, A3, .......

Question

Let A1, A2, A3, ....... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = $${1 \over {1296}}$$ and A2 + A4 = $${7 \over {36}}$$, then the value of A6 + A8 + A10 is equal to

Accepted Answer

$${{{A_4}} \over {{r^3}}}.\,{{{A_4}} \over r}.\,{A_4}r\,.\,{A_4}{r^3} = {1 \over {1296}}$$

$${A_4} = {1 \over 6}$$

$${A_2} = {7 \over {36}} - {1 \over 6} = {1 \over {36}}$$

So $${A_6} + {A_8} + {A_{10}} = 1 + 6 + 36 = 43$$

Solutions · 1