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Geometric Progression 



Problem 1 of 23 


1. For given geometric progression series ,... find th term and addition of first th terms.










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Geometric Progression 
1. For given geometric progression series 3,6,12,24,48 ,... find 10 th term and addition of first 10 th terms.
Here `a = 3,`
`r = 6/3 = 2`
We know that, `a_n = a × r^(n1)`
`a_10 = 3 × 2^(10  1)`
`= 3 × 512`
`= 1536`
We know that, `S_n = a * (r^n  1)/(r  1)`
`:. S_10 = 3 × (2^10  1)/(2  1)`
`=> S_10 = 3 × (1024  1)/1`
`=> S_10 = 3 × 1023/1`
`=> S_10 = 3069`
Hence, `10^(th)` term of the given series is `1536` and sum of first `10^(th)` term is `3069`





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