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For a G.P. If t3 = 20 , t6 = 160 , find S7 - Mathematics and Statistics

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प्रश्न

For a G.P. If t3 = 20 , t6 = 160 , find S7

योग

उत्तर

t3 = 20, t6 = 160 

tn = arn–1

∴ t3 = ar3–1 = ar2

∴ ar2 = 20

∴ a = 20r2   ...(i)

Also, t6 = ar5

ar5 = 160

(20r2)r5 = 160    ...[From (i)]

∴ r3 = 16020 = 8

∴ r = 2

Substituting the value of r in (i) we get

a = 2022 = 5

Now, Sn = a(rn-1)r-1, for r > 1

∴ S7 = 5(27-1)2-1

= 5(128 – 1)

= 635

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अध्याय 2: Sequences and Series - Exercise 2.2 [पृष्ठ ३१]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 2 Sequences and Series
Exercise 2.2 | Q 4. (i) | पृष्ठ ३१

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