Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 4 - An Introduction to Functions - 4-7 Arithmetic Sequences - Practice and Problem-Solving Exercises - Page 281: 74


The common difference is $3a+2b$ The next term of the sequence: $7a + 5b + c+(3a+2b)=10a+7b+c$

Work Step by Step

We are given: $a + b + c, 4a + 3b + c, 7a + 5b + c, ... $ To find the pattern of this sequence we have to find the difference between consecutive terms of the sequence. 2nd term and 1st term: $4a + 3b + c -(a + b + c)=3a+2b$ 3rd term and 2nd term: $7a + 5b + c-(4a + 3b + c )=3a+2b$ The common difference is $3a+2b$. We use this pattern to get the next term of the sequence: $7a + 5b + c+(3a+2b)=10a+7b+c$
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