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Find How Many Terms of G.P 2/9 - 1/3 + 1/2.........Must Be Added to Get the Sum Equal to 5/72 - Mathematics

Sum

Find How many terms of G.P `2/9 - 1/3 + 1/2`.........must be added to get the sum equal to `55/72`?

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Solution

Given G.P. : `2/9-1/3+1/2`

Here,
First term, a = `2/9`

common ratio, r = `(-1/3)/(2/9)=-3/2<1`

Let required number of terms be n.

⇒ Sn = `55/72`

⇒`(a(1-r^n))/(1-r)=55/72`

⇒ `(2/9(1-(-3/2)^n))/(1-(-3/2))=55/72`

⇒ `(2/9(1-(-3/2)^n))/(5/2)=55/72`

⇒ `2/9(1-(-3/2)^n)=55/72xx5/2`

⇒ `1-(-3/2)^n=55/72xx5/2xx9/2`

⇒ `1-(-3/2)^n=275/32`

⇒ `1-275/32=(-3/2)^n`

⇒ `-275/32=(-3/2)^n`

⇒ `(-3/2)^5=(-3/2)^n`

⇒ n = 5

∴ Required number of terms = 5

Concept: Geometric Progression - Finding Sum of Their First ‘N’ Terms
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 10 | Page 161
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