Find the indicated partial sum for the given sequence.
-$\mathrm { s } _ { 4 } , 81,243,729,2187 , \ldots$
A) $- \frac { 1053 } { 2 }$
B) 9801
C) 2187
D) 3240

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence where each term is 3 times the previous term, starting with 81. The first term $a = 81$, and the common ratio $r = 3$. The formula for the sum of the first $n$ terms of a geometric sequence is $S_n = a \frac{1 - r^n}{1 - r}$. For $n = 4$, $S_4 = 81 \frac{1 - 3^4}{1 - 3} = 81 \frac{1 - 81}{-2} = 81 \times 40 = 3240$.

Find the Indicated Partial Sum for the Given Sequence s4,81,243,729,2187,…\mathrm { s } _ { 4 } , 81,243,729,2187 , \ldotss4​,81,243,729,2187,…

Find the Indicated Partial Sum for the Given Sequence $\mathrm { s } _ { 4 } , 81,243,729,2187 , \ldots$