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.
$S_{29} = \dfrac{29}{2}(0.7+56.7)
\\S_{29}=\dfrac{29}{2}(57.4)
\\S_{29}=832.3$
