Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.1 - Sequences and Summation Notation - 12.1 Exercises - Page 850: 7

Answer

First Term: $a_{1}=5^{1}=5$ Second Term: $a_{2}=5^{2}=25$ Third Term: $a_{3}=5^{3}=125$ Fourth Term: $a_{4}=5^{4}=625$ Hundredth Term: $a_{100}=5^{100}$

Work Step by Step

The rule for the nth term of a sequence is a rule that allows an individual to find any term in that sequence simply by plugging in the appropriate term number. Given the rule for sequence X, for example, we can find every single term in that sequence. In exercise 7, we are given the rule for the nth term of a specific sequence: $a_{n}=5^n$ To evaluate the first four terms as well as the hundredth term, we must simply replace "n" with the number of the corresponding term. The solution is as follows: First Term: $a_{1}=5^{1}=5$ Second Term: $a_{2}=5^{2}=25$ Third Term: $a_{3}=5^{3}=125$ Fourth Term: $a_{4}=5^{4}=625$ Hundredth Term: $a_{100}=5^{100}$ As can be seen, replacing "n" with the term number allows us to easily calculate the value of any term in the sequence. This method may be applied to find the terms of any sequence as long as its rule is given.
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