Find the numerical answer to the summation given below. sum_(n=0)^(97)(6n+7) Answer:

Identify Common Difference and Terms: We need to find the sum of the arithmetic series given by the formula sum_(n=0)^(97)(6n+7). To do this, we will first identify the common difference and the number of terms in the series. The common difference is 6, and since we are starting from n=0 and going up to n=97, there are 98 terms in total.Split Summation into Two Parts: We can split the summation into two separate summations: one for the 6n term and one for the constant 7. This gives us sum_(n=0)^(97)6n + sum_(n=0)^(97)7.Calculate Sum of 6n Terms: Let's first calculate the sum of the 6n terms. The sum of an arithmetic series can be found using the formula S = (n/2)(first term + last term). The first term when n=0 is 6*0 = 0 and the last term when n=97 is 6*97 = 582. So we have S = (98/2)(0 + 582).Calculate Sum of Constant 7 Terms: Performing the calculation for the sum of the 6n terms, we get S = 49 * 582 = 28518.Add Two Sums for Total: Now we calculate the sum of the constant 7 terms. Since this is a constant added 98 times, the sum is simply 98 * 7.Performing the calculation for the sum of the constant 7 terms, we get 98 * 7 = 686.Finally, we add the two sums together to get the total sum of the series: 28518 + 686.Adding the two sums, we get 28518 + 686 = 29204. This is the sum of the series from n=0 to n=97 of the expression (6n+7).

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Find the numerical answer to the summation given below.

sum_(n=0)^(97)(6n+7)
Answer:

Find the numerical answer to the summation given below. $\newline$ $\sum_{n=0}^{97}(6 n+7)$ $\newline$ Answer:

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Algebra 2

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

\newline

\sum_{n=0}^{97}(6 n+7)

\newline

Answer:

Identify Common Difference and Terms: We need to find the sum of the arithmetic series given by the formula $\sum_{n=0}^{97}(6n+7)$ . To do this, we will first identify the common difference and the number of terms in the series. $\newline$ The common difference is $6$ , and since we are starting from $n=0$ and going up to $n=97$ , there are $98$ terms in total.
Split Summation into Two Parts: We can split the summation into two separate summations: one for the $6n$ term and one for the constant $7$ . This gives us $\sum_{n=0}^{97}6n + \sum_{n=0}^{97}7$ .
Calculate Sum of $6$ n Terms: Let's first calculate the sum of the $6n$ terms. The sum of an arithmetic series can be found using the formula $S = \frac{n}{2}(\text{first term} + \text{last term})$ . The first term when $n=0$ is $6\times 0 = 0$ and the last term when $n=97$ is $6\times 97 = 582$ . So we have $S = \frac{98}{2}(0 + 582)$ .
Calculate Sum of Constant $7$ Terms: Performing the calculation for the sum of the $6n$ terms, we get $S = 49 \times 582 = 28518$ .
Add Two Sums for Total: Now we calculate the sum of the constant $7$ terms. Since this is a constant added $98$ times, the sum is simply $98 \times 7$ .
Add Two Sums for Total: Now we calculate the sum of the constant $7$ terms. Since this is a constant added $98$ times, the sum is simply $98 \times 7$ .Performing the calculation for the sum of the constant $7$ terms, we get $98 \times 7 = 686$ .
Add Two Sums for Total: Now we calculate the sum of the constant $7$ terms. Since this is a constant added $98$ times, the sum is simply $98 \times 7$ .Performing the calculation for the sum of the constant $7$ terms, we get $98 \times 7 = 686$ .Finally, we add the two sums together to get the total sum of the series: $28518 + 686$ .
Add Two Sums for Total: Now we calculate the sum of the constant $7$ terms. Since this is a constant added $98$ times, the sum is simply $98 \times 7$ .Performing the calculation for the sum of the constant $7$ terms, we get $98 \times 7 = 686$ .Finally, we add the two sums together to get the total sum of the series: $28518 + 686$ .Adding the two sums, we get $28518 + 686 = 29204$ . This is the sum of the series from $n=0$ to $n=97$ of the expression $(6n+7)$ .