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Question
In a G.P. the 9th term is 32805 and 6th term is 1215. Find the 12th term
Solution
Given, 9th term = 32805
a.rn–1 = `1/2817`
t9 = 32805 [tn = arn–1]
a.r8 = 32805 …(1)
6th term = 1215
a.r5 = 1215 …(2)
Divide (1) by (2)
`("ar"^8)/("ar"^5) = 32805/1215`
⇒ r3 = `6561/243`
= `2187/81`
= `729/27`
= `243/9`
= `81/3`
r3 = 27
⇒ r3 = 33
r = 3
Substitute the value of r = 3 in (2)
a.35 = 1215
a × 243 = 1215
a = `1215/243` = 5
Here a = 5, r = 3, n = 12
t12 = `5 xx 3^((12 - 1))`
= 5 × 311
∴ 12th term of a G.P. = 5 × 311
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