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Question
Find the number of terms in the following G.P.
`1/3, 1/9, 1/27, ..., 1/2187`
Sum
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Solution
`1/3, 1/9, 1/27, ..., 1/2187`
| Hint: | |
| 3 | 729 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 | |
Here a = `1/3`, r = `(1/9)/(1/3)`
= `1/9 xx 3/1`
= `1/3`
tn = arn–1
`1/3 xx (1/3)^("n" - 1)`
= `1/2817`
`(1/3)^("n" - 1) = 1/2817 xx 3`
= `1/729`
`(1/3)^("n" - 1) = 1/3^6`
= `(1/3)^6`
n – 1 = 6
n = 6 + 1 = 7
∴ No. of terms = 7
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