Pregunta
Find the sum. \( \sum_{k=3}^{6}(5 k-2)=\square \)
Ask by Watson Garrett. in the United States
Mar 21,2025
Solución de inteligencia artificial de Upstudy
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The sum is 82.
Solución
We start with the sum:
\[
\sum_{k=3}^{6} (5k - 2)
\]
This means we sum the expression \(5k - 2\) for \(k = 3, 4, 5, 6\).
1. For \(k = 3\):
\[
5(3) - 2 = 15 - 2 = 13
\]
2. For \(k = 4\):
\[
5(4) - 2 = 20 - 2 = 18
\]
3. For \(k = 5\):
\[
5(5) - 2 = 25 - 2 = 23
\]
4. For \(k = 6\):
\[
5(6) - 2 = 30 - 2 = 28
\]
Now, add all these values:
\[
13 + 18 + 23 + 28 = 82
\]
Thus, the sum is \(\boxed{82}\).
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Simplifique esta solución The Deep Dive
To find the sum \( \sum_{k=3}^{6}(5 k-2) \), we evaluate the expression for each integer \( k \) from 3 to 6. 1. For \( k = 3 \): \[ 5(3) - 2 = 15 - 2 = 13 \] 2. For \( k = 4 \): \[ 5(4) - 2 = 20 - 2 = 18 \] 3. For \( k = 5 \): \[ 5(5) - 2 = 25 - 2 = 23 \] 4. For \( k = 6 \): \[ 5(6) - 2 = 30 - 2 = 28 \] Now, let's add all these results together: \[ 13 + 18 + 23 + 28 \] Calculating the sum step by step: \[ 13 + 18 = 31 \] \[ 31 + 23 = 54 \] \[ 54 + 28 = 82 \] Thus, the sum \( \sum_{k=3}^{6}(5 k-2) = 82 \). So, the final answer is: \[ \boxed{82} \]
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