Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 9 - Sequences and Series - 9-1 Mathematical Patterns - Practice and Problem-Solving Exercises - Page 569: 16


Next three terms: 128, 256, and 512 Formula: $a_{1}$=4 $a_{n}$=$2a_{n-1}$

Work Step by Step

Looking at the problem, we see that neither addition nor subtraction will work since the numbers are getting exponentially bigger; therefore, we need to find a ratio of two terms, namely the second and first, third and second, third and fourth, etc... We see $\frac{8}{4}$=2, then $\frac{16}{8}$=2, and $\frac{32}{16}$=2. Through this, we see 2 is the constant number, or the number that is used to multiply the numbers in the sequence to gain the next value in the set. We know $a_{1}$=4, then we need to find a formula for the next numbers in the set. Since the next term is two times the previous term, the formula should be: $a_{n}$=$2a_{n-1}$, The next three terms are: $64(2)=128 \\128(2)=256) \\256(2) = 512$
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