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Geometric progression

This calculator computes n-th term and sum of geometric progression
Timur2011-07-16 04:17:35

Geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio.

If module of common ratio is greater than 1 progression shows exponential growth of terms towards infinity, if it is less than 1, but not zero, progression shows exponential decay of terms towards zero.

N-th term of the progression is found as
a_n=a_1q^{n-1}

Partial sum to n
S_n=\frac{a_nq-a_1}{q-1}=\frac{a_1-a_nq}{1-q}
where q is not equal to 1

For q =1
S_n=na_1

The number of terms in infinite geometric progression will approach to infinity n = \infty. Sum of infinite geometric progression can only be defined if common ratio is at the range from -1 to 1 inclusive.

S=\frac{a_1}{1-q}

Geometric progressionCreative Commons Attribution/Share-Alike License 3.0 (Unported)
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