## College Algebra 7th Edition

Published by Brooks Cole

# Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises - Page 607: 61

#### Answer

$S_{29}=832.3$

#### Work Step by Step

RECALL: (1) The sum of the first $n$ terms of an arithmetic sequence is given by the formula: $S_n=\dfrac{n}{2}(a+a_n)$ where $a$ = first term $d$ = common difference $a_n$ = $n^{th}$ term (2) The $n^{th}$ term $a_n$ of an arithmetic sequence is given by the formula: $a_n = a + (n-1)d$ where $a$ = first term $d$ = common difference The given arithmetic sequence has: $a=0.7 \\a_n = 56.7 \\d=2.7-0.7=2$ The formula for the partial sum requires the values of $a$, $a_n$ and $n$. However, only $a$ and $a_n$ are known at the moment. Solve for $n$ using the formula for $a_n$ to obtain: $\require{cancel} a_n = a + (n-1)d \\56.7 = 0.7+(n-1)(2) \\56.7-0.7 = (n-1)(2) \\56=(n-1)(2) \dfrac{56}{2}=\dfrac{(n-1)(2)}{2} \\28=n-1 \\28+1=n-1+1 \\29=n$ Now that it is known that $n=29$, the sum of the first 29 terms can be computed using the formula above. $S_{29} = \dfrac{29}{2}(0.7+56.7) \\S_{29}=\dfrac{29}{2}(57.4) \\S_{29}=832.3$

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