if third of a.p is four time the first term and 6th terms is 17 .find the progression.
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Consider a G.P series where first term is 'a' and common difference is 'r'
Let the series be a, ar,ar^2,ar^3 and so on..
3rd term=12=ar^2
6th term=96=ar^5
Dividing ar^5/ar^2, we get r^3=8=2^3
Therefore r=2
And, a=3
The terms are: 3,6,12,24,48,96,192,384,768…. and so on
For finding the sum of the terms we use the formula, s=a*(1-r^n)/(1-r), where n is the number of terms
Therefore, s=3*(1–2^9)/(1–2)=1533
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