generalised formula for the series

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

Re: generalised formula for the series

Quote:

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 :

$\displaystyle 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 :

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

Re: generalised formula for the series