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 - Lesson Check: 8

Answer

Yes. We can use the explicit formula below to find the nth term of an arithmetic sequence with a first term A(1) and a common difference d, by using the distributive property and by factoring out the common factor of d in the equation. Because: A(n) = A(1) + nd - d = A(1) + d (n - 1)

Work Step by Step

Yes. We can use the explicit formula below to find the nth term of an arithmetic sequence with a first term A(1) and a common difference d, by using the distributive property and by factoring out the common factor of d in the equation. Given the equation A(n) = A(1) + nd - d We see that +nd and -d both have a common +d variable so we can factor out the +d from the two terms which gives us the equation. A(n) = A(1) + d (n - 1) And thus we can find the nth term of the sequence.
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