Question

Find the sum of $S={\sum }_{k=1}^6{3}^{k-1}$

• A. $264$
• B. $362$
• C. $364$
• D. $464$

Answer 1

The correct option is C $364$

We first rewrite the sum $S$ as follows:

$S=1+3+9+27+81+243=364$

Another method is to first note that the terms making the sum are those of an arithmetic sequence with $a_1=1$ and $r=3$ using the formula $s_n=\frac{a_1(1-r^n)}{(1-r)}$ with $n=6$.

$\therefore s_6=\frac{1(1-3^6)}{(1-3)}=364$