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 280: 64


1. The explicit formula is A(n)=-10+4(n-1). The relationship between the first and second, and then second and third is that the magnitude of the values differs by 4 in each scenario and the previous term is less by 4.2. The recursive formula is A(n)=A(n-1)+4; A(1)=-10

Work Step by Step

A(n)=-10+4(n-1) 1. First term --> A(1)=-10+4(1-1) = -10+4(0) = -10 Second term --> A(2)=-10+4(2-1) = -10+4(1) = -10 +4 = -6 Difference by 4 as first term is 4 less than second term 2. Second term --> -6 Third term --> A(3)=-10+4(3-1) = -10+4(2) = -10 +8 = -2 Difference by 4 as second term is 4 less than third term 4. The recursive formula is A(n)=A(n-1)+4; A(1)=-10 Because the sequence is in the form of A(n)=A(n-1)+d and the value of A(1) is -10 which was derived using the explicit formula. The A(n-1) allows to find the value of previous term and the value of d which is 4 derived from the explicit formula is added to the previous term to find the value of the nth term.
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