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Question
Find the G.P. in which the 2nd term is `sqrt(6)` and the 6th term is `9sqrt(6)`
Solution
t2 = `sqrt(6)`
t6 = `9sqrt(6)`
tn = arn–1 in G.P.
∴ t2 = ar2–1 = `sqrt(6)`
ar = `sqrt(6)` ...(1)
t6 = ar6–1 = `9sqrt(6)`
ar5 = `9sqrt(6)` ...(2)
`((2))/((1)) = "ar"^5/"ar" = (9sqrt(6))/sqrt(6)`
r4 = 9
⇒ r2 = 3
⇒ r = `sqrt(3)`
Substitute r = `sqrt(3)` in (1)
ar = `sqrt(6)`
`"a"sqrt(3) = sqrt(6)`
a = `sqrt(6)/sqrt(3) = sqrt(6/3) = sqrt(2)`
∴ G.P. = a, ar, ar2, ...
= `sqrt(2), sqrt(6), sqrt(2) sqrt(3)^2, ...`
= `sqrt(2), sqrt(6), 3sqrt(2), ...`
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