Geometric Sum Formula
We have derived the expression for sum of a geometric series. Below is the formula for different common Ratio in a Geometric Series.
For Common Ratio < 1
Sn = a × (1 – rn)/(1 – r)
Where,
- Sn is sum of the GP upto n terms.
- a is the first term,
- r is the common ratio, and
- n is the number of terms up to which sum is required.
For Common Ratio > 1
Sn = a × (rn – 1)/(r – 1)
Where,
- Sn is sum of the GP upto n terms.
- a is the first term,
- r is the common ratio, and
- n is the number of terms up to which sum is required.
How to Find the Sum of Geometric Series
A geometric series is a sequence of numbers where each term after the first term is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In a geometric series, if the absolute value of the common ratio (∣r∣) is less than 1, the series converges to a finite value. Otherwise, it diverges (grows without bound). Let’s know more about sum of Geometric Series formula, derivation and examples in detail below.
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