Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
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Find the number of terms in the following G.P. 13,19,127,...,12187 - Mathematics

Sum

Find the number of terms in the following G.P.

`1/3, 1/9, 1/27, ..., 1/2187`

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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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APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 2 Numbers and Sequences
Exercise 2.7 | Q 5. (ii) | Page 72
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