Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# 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

#### 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