Let a1, a2, .

Question

Let a1, a2, . . . . . ., a10  be  a G.P.    If  $${{{a_3}} \over {{a_1}}} = 25,$$  then $${{{a_9}} \over {{a_5}}}$$ equals

Accepted Answer

a1, a2, . . . . ., a10  are in G.P.,

Let the common ratio be r

$${{{a_3}} \over {{a_1}}} = 25 \Rightarrow {{{a_1}{r^2}} \over {{a_1}}} = 25 \Rightarrow {r^2} = 25$$

$${{{a_9}} \over {{a_5}}} = {{{a_1}{r^8}} \over {{a_1}{r^4}}} = {r^4} = {5^4}$$

Solutions · 1