Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.3 Geometric Sequences; Geometric Series - 12.3 Assess Your Understanding - Page 825: 69


Arithmetic Sum: $1375$

Work Step by Step

We are given the sequence: $\{n+2\}$ Compute the difference between two consecutive terms: $(k+2)-((k-1)+2)=(k+2)-(k+1)=1$ As the difference between any consecutive terms is constant, the sequence is ARITHMETIC. Determine its first element and common difference: $a_1=1+2=3$ $d=1$ Compute the sum of the first 50 terms: $S_n=\dfrac{n(2a_1+(n-1)d)}{2}$ $S_{50}=\dfrac{50(2(3)+(50-1)(1)}{2}=1375$
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