Find the sum
\[
\sum_{n=11}^{80} 3 n=
\]

Answer

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Answer

The sum of the series is \(\boxed{9555}\).

Steps

Step 1 ：First, we identify the first term \(a_1\) as \(3*11 = 33\), the last term \(a_n\) as \(3*80 = 240\), and the number of terms \(n\) as \(80 - 11 + 1 = 70\).

Step 2 ：We then use the formula for the sum of an arithmetic series: \(\frac{n}{2} * (a_1 + a_n)\).

Step 3 ：Substituting the values we have: \(\frac{70}{2} * (33 + 240)\).

Step 4 ：Finally, we calculate the sum to get the final answer.

Step 5 ：The sum of the series is \(\boxed{9555}\).

Find the sum\[\sum_{n=11}^{80} 3 n=\]

Answer

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Find the sum
\[
\sum_{n=11}^{80} 3 n=
\]