Answer
arithmetic,
$71.5$
Work Step by Step
An arithmetic sequence has a common difference
$a_{n}=a+(n-1)d, $with nth partial sum:
1. $ S_{n}=\displaystyle \frac{n}{2}[2a+(n-1)d]\qquad$ or
2. $S_{n}=n(\displaystyle \frac{a+a_{n}}{2})$
A geometric sequence has a common ratio
$a_{n}=ar^{n-1}$, with nth partial sum:
$S_{n}=a\displaystyle \cdot\frac{1-r^{n}}{1-r}$
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Testing for common difference:
$3.7-3=0.7,\qquad 4.4-3.7=0.7,$
There is a common difference, the sequence is arithmetic,
$a=3$ and $d=0.7$
$a_{n}=3+0.7(n-1)$
The last term is 10, from which we find n
(the number of terms in the sum)
$3+0.7(n-1)=10\qquad /-3$
$0.7 (n-1)=7\qquad /\div 0.7$
$n-1=10$
$n=11$.
So, the sum equals
$S_{11}=\displaystyle \frac{11}{2}(3+10)=\frac{143}{2}=71.5$.
