# problem on A.P/G.P

• Jun 7th 2008, 03:09 AM
somnath6088
problem on A.P/G.P
Please solve the problem for me
Find the sum of the series
3+7+14+27+52+...................up to nth terms
• Jun 7th 2008, 03:30 AM
mr fantastic
Quote:

Originally Posted by somnath6088
Please solve the problem for me
Find the sum of the series
3+7+14+27+52+...................up to nth terms

The nth term in the series is given by the recurrence relation $a_n = 2 a_{n-1} - n + 3$ with $a_1 = 3$. This does not define an Arithmetic Sequence or a Geometric Sequence.

So I don't know why you would imply the series is arithmetic or geometric in your descriptive title of the problem.

Once you've got the nth term of the series in terms of n, you'll have more luck finding the value of the series.
• Jun 7th 2008, 03:36 AM
somnath6088
sorry.
the problem is
1+3+7+14+27+52+........up to nth terms.
• Jun 7th 2008, 03:37 AM
wingless
• Jun 7th 2008, 03:45 AM
wingless
3 + 7 + 14 + 27 + 52 + ...

$a_n = 3\cdot 2^n + n$ (starting from $a_0$)

$S_n = \sum_{k=0}^{n}3\cdot 2^k + k$

$S_n = 3\sum_{k=0}^{n}2^k +\sum_{k=0}^{n}k$

$S_n = 3\cdot (2^{n+1}-1) + \frac{n(n+1)}{2}$

You can add +1 to $S_n$ if you want to sum 1+3+7+14+27+...
• Jun 7th 2008, 03:51 AM
mr fantastic
Quote:

Originally Posted by mr fantastic
The nth term in the series is given by the recurrence relation $a_n = 2 a_{n-1} - n + 3$ with $a_1 = 3$. This does not define an Arithmetic Sequence or a Geometric Sequence.

So I don't know why you would imply the series is arithmetic or geometric in your descriptive title of the problem.

Once you've got the nth term of the series in terms of n, you'll have more luck finding the value of the series.

The nth term in the series (the original, not the revised) is $\frac{3}{2} \, (2^n) + n - 1$ (starting from n = 1). Others will benefit from knowing the correct series and might have more to say. I'll just give this reply to complement my first.

And in fact, you can still use this result. Use it to get the sum and then just add 1 to the result.