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How Many Terms of the Geometric Progression 1 + 4 + 16 + 64 + …….. Must Be Added to Get Sum Equal to 5461? - Mathematics

Sum

How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?

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Solution

Given G.P. : 1 + 4 + 16 + 64 +...........
Here,
first term, a = 1
common ratio, r = `4/1=4` (r > 1)
Let the number of terms to be added = n
Then, Sn = 5461

`=>(a(r^n-1))/(r-1)=5461`

`=> (1(4^"th"-1))/(4-1)=5461`

`=>(4^"th"-1)/3=5461`

⇒ 4th - 1 = 16383

⇒ 4th = 16384

⇒ n = 7

Hence, required number of terms = 7

Concept: Simple Applications - Geometric Progression
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 2 | Page 161
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