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For given geometric progression series 3,6,12,24,48 ,... then find n such that S(n) = 3069 .

Solution:
Your problem `->` For given geometric progression series 3,6,12,24,48 ,... then find n such that S(n) = 3069 .


Here `a = 3,`

`r = 6/3 = 2`

We know that, `S_n = a * (r^n - 1)/(r - 1)`

`=> S_n = 3 × ((2)^n - 1) / (2 - 1)`

`=> 3069 = 3 × ((2)^n - 1)/(1)`

`=> 2^n - 1 = 3069 × (1) / 3`

`=> 2^n - 1 = 1023`

`=> 2^n = 1024`

`=> 2^n = 2^10`

`=> n = 10`






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