# Find the sum of 3+7+14+27+52 +...... to n terms?

Given:

Note that no finite initial sequence determines the following terms without further information. So it could continue in any way.

That having been said, we can try to match the given terms with some kind of regular formula.

We could choose to match the given terms with a polynomial formula, which would be one possibility, but let us look for a simpler pattern.

Note that the terms of the sequence roughly double each time, so let's try subtracting the geometric progression:

The result is:

For geometric progressions we have:

and for arithmetic progressions we have:

So

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The sum of the series 3 + 7 + 14 + 27 + 52 + ... to n terms is given by the formula: S_n = 2n^3 - 3n^2 + n.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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