Asked by Vanderkinter Travels on May 31, 2024
Verified
Find a formula for the n th term of the geometric sequence. Assume that n begins with 1. a1=3,r=74a_{1}=3, r=\frac{7}{4}a1=3,r=47
A) an=3(74) n−1a_{n}=3\left(\frac{7}{4}\right) ^{n-1}an=3(47) n−1
B) an=(214) n−1a_{n}=\left(\frac{21}{4}\right) ^{n-1}an=(421) n−1
C) an=(74) na_{n}=\left(\frac{7}{4}\right) ^{n}an=(47) n
D) an=(214) na_{n}=\left(\frac{21}{4}\right) ^{n}an=(421) n
E) an=3(74) na_{n}=3\left(\frac{7}{4}\right) ^{n}an=3(47) n
Geometric Sequence
A succession of numbers where, from the second element onwards, each number is derived by multiplying its precursor by a steady, non-zero coefficient known as the common ratio.
Nth Term
The term that appears in a sequence's nth position, often defined by a formula that relates the term's position in the sequence to its value.
Formula
A formula is a mathematical rule or relationship expressed in symbols.
- Utilize geometric progression equations to identify distinct elements and calculate their cumulative partial totals.
Verified Answer
JH
Jessica Heath
Jun 06, 2024
Final Answer :
A
Explanation :
The formula for the nth term of a geometric sequence is $a_{n}=a_{1}r^{n-1}$. Plugging in the given values, we get $a_{n}=3\left(\frac{7}{4}\right)^{n-1}$. Therefore, the correct choice is $\boxed{\textbf{(A)}}$.
Learning Objectives
- Utilize geometric progression equations to identify distinct elements and calculate their cumulative partial totals.