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