Sum of a Geometric Sequence
Calculate the value of the nth term of a geometric sequence and the sum of the terms from the first term to the nth term.
| \(\normalsize Sn=a+ar+ar^2+ar^3+\cdots +ar^{n-1}\\\) |
| nth term an | |
| Sum Sn of a geometric sequence |
| \(\normalsize Geometric\ progression\\ (1)\ a_n=ar^{n-1}\\ (2)\ Sn={\large \displaystyle \sum_{\small k=1}^{\small n}}ar^{k-1}\\ \hspace{45px} =a+ar+ar^2+ar^3+\cdots +ar^{n-1}\\ \hspace{45px} =\left\{\begin{array}{1}{\large\frac{a(1-r^n)}{1-r}\hspace{40px}r\neq 1}\\ \hspace{10px} {\normalsize na\hspace{70px}r=1}\end{array}\right.\\\) |
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