Find the numerical answer to the summation given below. sum_(n=6)^(61)(6n+7) Answer:

Calculate number of terms: We need to find the sum of the arithmetic series from n=6 to n=61 for the expression (6n+7). The general formula for the sum of an arithmetic series is S = n/2 * (a_1 + a_n), where n is the number of terms, a_1 is the first term, and a_n is the last term.Find first term: First, we calculate the number of terms in the series. Since the series starts at n=6 and ends at n=61, the number of terms is (61 - 6) + 1 = 56.Find last term: Next, we find the first term of the series by substituting n=6 into the expression (6n+7). This gives us a_1 = (6*6) + 7 = 43.Use sum formula: Now, we find the last term of the series by substituting n=61 into the expression (6n+7). This gives us a_n = (6*61) + 7 = 373.Perform calculations: We can now use the sum formula for an arithmetic series: S = n/2 * (a_1 + a_n). Substituting the values we have, S = 56/2 * (43 + 373).Performing the calculations, we get S = 28 * (416) = 11648.

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Find the numerical answer to the summation given below.

sum_(n=6)^(61)(6n+7)
Answer:

Find the numerical answer to the summation given below. $\newline$ $\sum_{n=6}^{61}(6 n+7)$ $\newline$ 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=6}^{61}(6 n+7)

\newline

Answer:

Calculate number of terms: We need to find the sum of the arithmetic series from $n=6$ to $n=61$ for the expression $(6n+7)$ . The general formula for the sum of an arithmetic series is $S = \frac{n}{2} * (a_1 + a_n)$ , where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term.
Find first term: First, we calculate the number of terms in the series. Since the series starts at $n=6$ and ends at $n=61$ , the number of terms is $(61 - 6) + 1 = 56$ .
Find last term: Next, we find the first term of the series by substituting $n=6$ into the expression $(6n+7)$ . This gives us $a_1 = (6\times 6) + 7 = 43$ .
Use sum formula: Now, we find the last term of the series by substituting $n=61$ into the expression $(6n+7)$ . This gives us $a_n = (6\times61) + 7 = 373$ .
Perform calculations: We can now use the sum formula for an arithmetic series: $S = \frac{n}{2} \times (a_1 + a_n)$ . Substituting the values we have, $S = \frac{56}{2} \times (43 + 373)$ .
Perform calculations: We can now use the sum formula for an arithmetic series: $S = \frac{n}{2} \times (a_1 + a_n)$ . Substituting the values we have, $S = \frac{56}{2} \times (43 + 373)$ .Performing the calculations, we get $S = 28 \times (416) = 11648$ .