problem on A.P/G.P

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June 7th 2008, 02:09 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
June 7th 2008, 02:30 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.
June 7th 2008, 02:36 AM
somnath6088

sorry.
the problem is
1+3+7+14+27+52+........up to nth terms.
June 7th 2008, 02:37 AM
wingless

Can you see the pattern?

http://img399.imageshack.us/img399/9440/yeyyyf6.png
June 7th 2008, 02:45 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+...
June 7th 2008, 02:51 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.