Asked by Zacharias Quintanilla on May 06, 2024
Verified
Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. 4,−10,25,−1252,…4,-10,25,-\frac{125}{2}, \ldots4,−10,25,−2125,…
A) an=2(−52) n−1a_{n}=2\left(-\frac{5}{2}\right) ^{n-1}an=2(−25) n−1
B) an=2(−52) n−2a_{n}=2\left(-\frac{5}{2}\right) ^{n-2}an=2(−25) n−2
C) an=4(−52) n−1a_{n}=4\left(-\frac{5}{2}\right) ^{n-1}an=4(−25) n−1
D) an=−2(−52) na_{n}=-2\left(-\frac{5}{2}\right) ^{n}an=−2(−25) n
E) an=−4(−52) na_{n}=-4\left(-\frac{5}{2}\right) ^{n}an=−4(−25) n
Geometric Sequence
A progression of numbers in which each term beyond the initial one is produced by the multiplication of the preceding term by a constant, non-zero multiplier called the common ratio.
Formula
A mathematical expression that describes a relationship among different quantities.
N Th Term
A formula that allows the calculation of any term in a sequence based on its position (n).
- Calculate geometric sequence terms and derive their formulas.
Verified Answer
KR
K R E A A T O R EMay 12, 2024
Final Answer :
C
Explanation :
The first term a1=4a_1 = 4a1=4 , and the common ratio r=−104=−52r = \frac{-10}{4} = -\frac{5}{2}r=4−10=−25 . Thus, the formula for the nth term is an=4(−52)n−1a_n = 4\left(-\frac{5}{2}\right)^{n-1}an=4(−25)n−1 .
Learning Objectives
- Calculate geometric sequence terms and derive their formulas.