Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 11 - Section 11.1 - Sequences and Summation Notation - Exercise Set - Page 829: 47



Work Step by Step

Since, we have $a+(a+d)+(a+2d)+.....(a+nd)$ This form a arithmetic progression sequence whose first term is $a$ with common difference of $d$. for this , we have $a_n=a+(k-1)d$; for k-th term Last term becomes $a+(k-1)d=a+nd$ or, $k=n+1$ Hence, $a+ar+ar^^{14}$ can be summed up with the summation notation as: $\sum_{k=1}^{(n+1)}[a+(k-1)d]$
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