Answer
$832.3$
Work Step by Step
See p. 855.
For the arithmetic sequence $a_{n}=a+(n-1)d$
the nth partial sum $S_{n}=\displaystyle \sum_{k=1}^{n}[a+(k-1)d]$
is given by either of the following equivalent formulas:
1. $S_{n}=\displaystyle \frac{n}{2}[2a+(n-1)d]\qquad $2. $S_{n}=n(\displaystyle \frac{a+a_{n}}{2})$
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We see from the given sequence that
$a=0.7$
$d=2.7-0.7=2$
The last term is $a_{n}=56.7$ (we find n):
$a_{n}=a+(n-1)d$
$56.7=0.7+2(n-1)\qquad/-0.7$
$56=2(n-1)\qquad/\div 2$
$28=n-1$
$29=n$
Finally, we find $S_{29}$, (using formula 2)
$S_{29}=29(\displaystyle \frac{0.7+56.7}{2})=832.3$