Geometric Progression

Question

The sum of the first n terms of a GP is S = a(rⁿ - 1)/(r - 1) when

RankGuru · Accepted Answer

1. **Formula Derivation**: The formula $S_n = a \frac{r^n - 1}{r - 1}$ is derived by subtracting $rS_n$ from $S_n$. 
2. **Constraint**: If $r = 1$, the denominator $r - 1$ becomes zero, making the expression undefined.
3. **Exception Case**: When $r = 1$, the sequence is $a, a, a, \dots$, and the sum is simply $n 	imes a$.
4. **Applicability**: Thus, the standard fraction formula applies only when **$r 
eq 1$**.

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