Find the numerical answer to the summation given below. sum_(n=1)^(78)(7n+6) Answer:

Recognize Parts: Recognize that the summation of the series can be separated into two parts: the summation of 7n and the summation of 6. This gives us sum_(n=1)^(78)7n + sum_(n=1)^(78)6.Evaluate First Part: Evaluate the first part of the summation sum_(n=1)^(78)7n. This is a sum of an arithmetic series, which can be calculated using the formula for the sum of the first n terms of an arithmetic series: S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the last term. In this case, a_1 = 7*1 and a_n = 7*78.Calculate First Part: Calculate the sum of the first part using the formula from Step 2. S_n = 78/2 * (7*1 + 7*78) = 39 * (7 + 546) = 39 * 553 = 21567Evaluate Second Part: Evaluate the second part of the summation sum_(n=1)^(78)6. Since 6 is a constant, the sum is simply 6 * 78.Calculate Second Part: Calculate the sum of the second part. 6 * 78 = 468Add Results: Add the results from Step 3 and Step 5 to get the final answer. 21567 + 468 = 22035

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Find the numerical answer to the summation given below.

sum_(n=1)^(78)(7n+6)
Answer:

Find the numerical answer to the summation given below. $\newline$ $\sum_{n=1}^{78}(7 n+6)$ $\newline$ Answer:

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Algebra 2

Sum of finite series starts from 1

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Q. Find the numerical answer to the summation given below.

\newline

\sum_{n=1}^{78}(7 n+6)

\newline

Answer:

Recognize Parts: Recognize that the summation of the series can be separated into two parts: the summation of $7n$ and the summation of $6$ . This gives us $\sum_{n=1}^{78}7n + \sum_{n=1}^{78}6$ .
Evaluate First Part: Evaluate the first part of the summation $\sum_{n=1}^{78} 7n$ . This is a sum of an arithmetic series, which can be calculated using the formula for the sum of the first $n$ terms of an arithmetic series: $S_n = \frac{n}{2} \times (a_1 + a_n)$ , where $a_1$ is the first term and $a_n$ is the last term. In this case, $a_1 = 7 \times 1$ and $a_n = 7 \times 78$ .
Calculate First Part: Calculate the sum of the first part using the formula from Step $2$ . $\newline$ $S_n = \frac{78}{2} \times (7\times1 + 7\times78)$ $\newline$ $= 39 \times (7 + 546)$ $\newline$ $= 39 \times 553$ $\newline$ $= 21567$
Evaluate Second Part: Evaluate the second part of the summation $\sum_{n=1}^{78} 6$ . Since $6$ is a constant, the sum is simply $6 \times 78$ .
Calculate Second Part: Calculate the sum of the second part. $\newline$ $6 \times 78 = 468$
Add Results: Add the results from Step $3$ and Step $5$ to get the final answer. $21567 + 468 = 22035$