What is the sum of the first five terms of the series 35 + 30 + 25 + . . . ?
We notice that we can find a pattern by subtracting 5 from each term. This gives us the arithmetic sequence $35, 30, 25, \ldots$. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the desired sum is $(35 + 25)/2 \cdot 5 = \boxed{150}$.
are you sure
Apologies for the confusion in my previous response. I made an error in the pattern analysis.
To find the sum of the first five terms of the series $35 + 30 + 25 + \ldots$, we notice that the terms form an arithmetic sequence with a common difference of $-5$. We can find the sum by using the formula for the sum of an arithmetic series:
$S = \frac{n}{2}(a_1 + a_n)$,
where $S$ is the sum of the series, $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term.
In this series, the first term $a_1 = 35$, and the last term $a_n = 35 + (n-1)(-5)$, where $n$ is the number of terms. Substituting these values into the formula, we have:
$S = \frac{5}{2}(35 + (5-1)(-5)) = \frac{5}{2}(35 + 4(-5)) = \frac{5}{2}(35 - 20) = \frac{5}{2}(15) = \boxed{37.5}$.