Find the sum of the finite arithmetic series. 10 ∑ n=1 (7n+4)

Arithmetic Series Sum Formula: To find the sum of an arithmetic series, we can use the formula S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term. In this case, we need to find the sum of the first 10 terms of the series where each term is given by 7n+4.Find First Term: First, we need to find the first term a_1 by plugging n=1 into the formula 7n+4. This gives us a_1 = 7(1) + 4 = 11.Find Tenth Term: Next, we need to find the tenth term a_10 by plugging n=10 into the formula 7n+4. This gives us a_10 = 7(10) + 4 = 70 + 4 = 74.Calculate Sum: Now that we have the first term a_1 and the tenth term a_10, we can use the sum formula S_n = n/2 * (a_1 + a_n). Plugging in the values, we get S_10 = 10/2 * (11 + 74).Final Result: Simplifying the expression, we get S_10 = 5 * (11 + 74) = 5 * 85 = 425.

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Algebra 2

Find the sum of an arithmetic series

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Q. Find the sum of the finite arithmetic series.

\sum_{n=1}^{10} (7n+4)

\newline

______

Arithmetic Series Sum Formula: To find the sum of an arithmetic series, we can use the formula $S_n = \frac{n}{2} * (a_1 + a_n)$ , where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, and $a_n$ is the $n$ th term. In this case, we need to find the sum of the first $10$ terms of the series where each term is given by $7n+4$ .
Find First Term: First, we need to find the first term $a_1$ by plugging $n=1$ into the formula $7n+4$ . This gives us $a_1 = 7(1) + 4 = 11$ .
Find Tenth Term: Next, we need to find the tenth term $a_{10}$ by plugging $n=10$ into the formula $7n+4$ . This gives us $a_{10} = 7(10) + 4 = 70 + 4 = 74$ .
Calculate Sum: Now that we have the first term $a_1$ and the tenth term $a_{10}$ , we can use the sum formula $S_n = \frac{n}{2} * (a_1 + a_n)$ . Plugging in the values, we get $S_{10} = \frac{10}{2} * (11 + 74)$ .
Final Result: Simplifying the expression, we get $S_{10} = 5 \times (11 + 74) = 5 \times 85 = 425$ .