College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.1 - Sequences - 9.1 Assess Your Understanding: 30

Answer

$a_n=\left(\dfrac{2}{3}\right)^n$

Work Step by Step

The pattern shows that: (1) The numerators involve powers of $2$. first term's numerator = $2^1=2$ second term's numerator = $2^2=4$ third term's numerator = $2^3=8$ fourth term's numerator = $2^4=16$ (2) The denominators involve powers of $3$: first term's denominator = $3^1 = 3$ second term's denominator = $3^2 =9$ third term's denominator = $3^3 = 27$ fourth term's denominator = $3^4=81$ Thus, the $n^{th}$ term of the sequence is: $a_n=\dfrac{2^n}{3^n}=\left(\dfrac{2}{3}\right)^n$
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