College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 45

Answer

$a=706\\ a_2=712$

Work Step by Step

RECALL: The $n^{th}$ $a_n$ of an arithmetic sequence is given by the formula: $a_n = a + d(n-1)$ where $a$ = first term $d$ = common difference The 50th term is 1000. Thus, $a_{50} = 1000$ and the common difference is $d=6$. Substitute these values to the formula above to obtain: $a_n = a + d(n-1) \\a_{50} = a + d(50-1) \\1000 = a + 6(49) \\1000 = a + 294 \\1000-294= a \\706 = a$ The second term can be found by adding the common difference to the first term. Thus, $a_2=706+6 \\a_2=712$ Therefore the first two terms of the sequence are: $a=706\\ a_2=712$
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