Maharashtra State BoardHSC Commerce 11th
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Verify whether the following sequences are G.P. If so, write tn : 5,15,155,1255, ... - Mathematics and Statistics

Sum

Verify whether the following sequence is G.P. If so, write tn: 

`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...

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Solution

`sqrt(5), 1/sqrt(5), 1/(5sqrt(5)), 1/(25sqrt(5))`, ...

t1 = `sqrt(5), "t"_2 = 1/sqrt(5), "t"_3 = 1/(5sqrt(5)), "t"_4 = 1/(25sqrt(5)`, ...

Here, `"t"_2/"t"_1 = "t"_3/"t"_2 = "t"_4/"t"_3 = 1/5`

Since, the ratio of any two consecutive terms is a constant, the given sequence is a geometric progression.

Here, a = `sqrt(5), "r" = 1/5`

tn = arn–1

∴ tn = `sqrt(5) (1/5)^("n" - 1)`

= `(5)^(1/2) (5)^(1 - "n")`

= `(5)^(3/2 - "n")`.

Concept: Sequence and Series - Geometric Progression (G.P.)
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 4 Sequences and Series
Exercise 4.1 | Q 1. (iii) | Page 50
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