Find the numerical answer to the summation given below. sum_(n=0)^(98)(7n+6) Answer:

Recognize Linear Expression Split: Recognize that the summation is of a linear expression in terms of n. The summation can be split into two separate summations: one for the 7n term and one for the constant term 6.Apply Summation Rule Linear Term: Apply the summation rule for the first term, which is a linear term 7n. The sum of an arithmetic series is given by the formula sum_(n=0)^(k)(an) = a * (k * (k + 1)) / 2, where a is the constant multiplier of n. In this case, a = 7 and k = 98.Calculate Sum First Term: Calculate the sum of the first term using the formula from Step 2. sum_(n=0)^(98)(7n) = 7 * (98 * (98 + 1)) / 2 = 7 * (98 * 99) / 2 = 7 * (9702) / 2 = 7 * 4851 = 33957Apply Summation Rule Constant Term: Apply the summation rule for the second term, which is a constant term 6. The sum of a constant series is given by the formula sum_(n=0)^(k)(c) = c * (k + 1), where c is the constant term. In this case, c = 6 and k = 98.Calculate Sum Second Term: Calculate the sum of the second term using the formula from Step 4. sum_(n=0)^(98)(6) = 6 * (98 + 1) = 6 * 99 = 594Add Final Results: Add the results from Step 3 and Step 5 to get the final answer. Final Sum = 33957 + 594 = 34551

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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.

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\sum_{n=0}^{98}(7 n+6)

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Answer:

Recognize Linear Expression Split: Recognize that the summation is of a linear expression in terms of $n$ . The summation can be split into two separate summations: one for the $7n$ term and one for the constant term $6$ .
Apply Summation Rule Linear Term: Apply the summation rule for the first term, which is a linear term $7n$ . The sum of an arithmetic series is given by the formula $\sum_{n=0}^{k}(an) = a \cdot \left(\frac{k \cdot (k + 1)}{2}\right)$ , where $a$ is the constant multiplier of $n$ . In this case, $a = 7$ and $k = 98$ .
Calculate Sum First Term: Calculate the sum of the first term using the formula from Step $2$ . $\newline$ $\sum_{n=0}^{98}(7n) = 7 \times (98 \times (98 + 1)) / 2$ $\newline$ $= 7 \times (98 \times 99) / 2$ $\newline$ $= 7 \times (9702) / 2$ $\newline$ $= 7 \times 4851$ $\newline$ $= 33957$
Apply Summation Rule Constant Term: Apply the summation rule for the second term, which is a constant term $6$ . The sum of a constant series is given by the formula $\sum_{n=0}^{k}(c) = c \cdot (k + 1)$ , where $c$ is the constant term. In this case, $c = 6$ and $k = 98$ .
Calculate Sum Second Term: Calculate the sum of the second term using the formula from Step $4$ . $\newline$ $\sum_{n=0}^{98}(6) = 6 \times (98 + 1)$ $\newline$ $= 6 \times 99$ $\newline$ $= 594$
Add Final Results: Add the results from Step $3$ and Step $5$ to get the final answer. $\newline$ Final Sum = $33957 + 594$ $\newline$ = $34551$