The `5^(t h)`, `8^(t h)`and `11^(t h)`terms of a G.P. are p, q and s, respectively. Show that `q^2=p s`.

Answer

N/a

Explanation

Let first term be 'a' and common ratio be 'r' of the given G.P.
`therefore" 5th term of G.P. p="ar^(5-1)=ar^(4)," ....(1)"`
`therefore" 8th term of G.P. q="ar^(8-1)=ar^(7)," ....(2)"`
`therefore" 11th term of G.P. s="ar^(11-1)=ar^(10)," ....(3)"`
Multiply equation (1) and equation (3)
`ar^(4)xxar^(10)=ps`
`rArr" "a^(2)r^(14)=psrArr(ar^(7))^(2)=ps`
`"From equation (2), "q^(2)=ps`