generalised formula for the series

**pranay** · March 12th 2012, 03:11 PM

Hi, given the property for a series such that the second term is got by adding a constant 'd' to the 1st term and the 3rd term is got by multiplying the 2nd term by another constant 'r' and so on ..how can we arrive at a generalised formula for nth term of the series if we are given the 1st term , d and r?
E.g if first term = 2, d = 2 ,r = 3 then the series is :
2,4,12,14,42,44,132,134,...
so the 4th term is 14, 7th term is 132 and so on..
Thanks

**princeps** · March 12th 2012, 11:09 PM

Originally Posted by pranay

Hi, given the property for a series such that the second term is got by adding a constant 'd' to the 1st term and the 3rd term is got by multiplying the 2nd term by another constant 'r' and so on ..how can we arrive at a generalised formula for nth term of the series if we are given the 1st term , d and r?
E.g if first term = 2, d = 2 ,r = 3 then the series is :
2,4,12,14,42,44,132,134,...
so the 4th term is 14, 7th term is 132 and so on..
Thanks

A) If n is an even number :

$a_n=a_1 \cdot r^{\frac{n-2}{2}}+d \cdot \displaystyle \sum_{i=0}^{\frac{n-2}{2}} r^i$

B) If n is an odd number :

$a_n=a_1 \cdot r^{\frac{n-1}{2}}+d \cdot \displaystyle \sum_{i=1}^{\frac{n-1}{2}} r^i$

**pranay** · March 13th 2012, 01:03 AM

Thanks a lot princeps

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