Asked by Kevin Brown on Mar 10, 2024



Find the n th partial sum of the geometric sequence. 5,15,45,135,405,…,n=75,15,45,135,405, \ldots, \quad n=75,15,45,135,405,,n=7

A) 1,820
B) 5,465
C) 200
D) 5,514
E) 5,808

Geometric Sequence

A sequence in which each number following the first is generated by multiplying the former number by a fixed, nonzero factor, this factor is identified as the common ratio.

Partial Sum

The sum of a portion of a sequence of terms, or a method of summing certain numbers by grouping.

N Th

Referring to an unspecified member of a series or set.

  • Understand the concept and computation of partial sums in geometric sequences.

Verified Answer

Abbey Marshall

Mar 10, 2024

Final Answer :
Explanation :
The given sequence is a geometric sequence with the first term a=5a = 5a=5 and common ratio r=3r = 3r=3 . The nth partial sum of a geometric sequence is given by Sn=a1−rn1−rS_n = a \frac{1-r^n}{1-r}Sn=a1r1rn for r≠1r \neq 1r=1 . Plugging in the values, we get S7=51−371−3=51−2187−2=5⋅1093=5465S_7 = 5 \frac{1-3^7}{1-3} = 5 \frac{1-2187}{-2} = 5 \cdot 1093 = 5465S7=513137=5212187=51093=5465 .