Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
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Find the sum of the Geometric series 3 + 6 + 12 + …….. + 1536 - Mathematics

Sum

Find the sum of the Geometric series 3 + 6 + 12 + …….. + 1536

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Solution

3 + 6 + 12 + …. + 1536

a = 3, r = `6/3` = 2

tn = 1536

a.rn–1 = 1536 ⇒ 3(2n–1) = 1536

2n–1 = `1536/3` ⇒ 2n–1 = 512

2n–1 =  29

∴ n – 1 = 9

n = 9 + 1 = 10

Number of terms = 10

Sn = `("a"("r"^"n" - 1))/("r" - 1)`

Sn = `(3(2^10 - 1))/(2 - 1)`

= `(3(1024 - 1))/1`

= 3 × 1023

= 3069

∴ Sum of the series is 3069

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APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 2 Numbers and Sequences
Exercise 2.8 | Q 7 | Page 76
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