Find the numerical answer to the summation given below. sum_(n=6)^(94)(5n+7) Answer:

Calculate First Term: To solve the summation, we need to find the sum of the arithmetic series from n=6 to n=94 of the expression 5n+7. The first term of the series when n=6 is 5(6)+7 = 37, and the last term when n=94 is 5(94)+7 = 477.Find Number of Terms: The sum of an arithmetic series can be found using the formula 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. To find the number of terms, we use the formula n = (last term - first term)/common difference + 1. Here, the common difference is 5 (since each term increases by 5n), so n = (94 - 6)/1 + 1 = 89.Calculate Sum: Now we can calculate the sum using the formula S = (n/2)(a_1 + a_n). Plugging in the values we have S = (89/2)(37 + 477).Final Calculation: Calculating the sum, we get S = (89/2)(514) = 44.5 * 514 = 22883.

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

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\sum_{n=6}^{94}(5 n+7)

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Answer:

Calculate First Term: To solve the summation, we need to find the sum of the arithmetic series from $n=6$ to $n=94$ of the expression $5n+7$ . The first term of the series when $n=6$ is $5(6)+7 = 37$ , and the last term when $n=94$ is $5(94)+7 = 477$ .
Find Number of Terms: The sum of an arithmetic series can be found using the formula $S = \frac{n}{2}(a_1 + a_n)$ , where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term. To find the number of terms, we use the formula $n = \frac{\text{last term} - \text{first term}}{\text{common difference}} + 1$ . Here, the common difference is $5$ (since each term increases by $5n$ ), so $n = \frac{94 - 6}{1} + 1 = 89$ .
Calculate Sum: Now we can calculate the sum using the formula $S = \frac{n}{2}(a_1 + a_n)$ . Plugging in the values we have $S = \frac{89}{2}(37 + 477)$ .
Final Calculation: Calculating the sum, we get $S = \left(\frac{89}{2}\right)(514) = 44.5 \times 514 = 22883$ .