Find the numerical answer to the summation given below. sum_(n=0)^(60)(4n+7) Answer:

Calculate number of terms: We need to find the sum of the arithmetic series given by the formula (4n+7) from n=0 to n=60. 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.Find first term: First, we calculate the number of terms in the series. Since the series starts at n=0 and ends at n=60, there are 60 - 0 + 1 = 61 terms.Find last term: Next, we find the first term of the series by substituting n=0 into the formula (4n+7). This gives us a_1 = 4(0) + 7 = 7.Use sum formula: Now, we find the last term of the series by substituting n=60 into the formula (4n+7). This gives us a_n = 4(60) + 7 = 240 + 7 = 247.Perform calculation: We can now use the sum formula for an arithmetic series: S = (n/2)(a_1 + a_n). Substituting the values we have, S = (61/2)(7 + 247).Multiply terms: Perform the calculation inside the parentheses first: 7 + 247 = 254.Find sum: Now, multiply the number of terms by the sum of the first and last term: S = (61/2) * 254.Perform the multiplication to find the sum of the series: S = 61 * 127 = 7747.

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Find the numerical answer to the summation given below.

sum_(n=0)^(60)(4n+7)
Answer:

Find the numerical answer to the summation given below. $\newline$ $\sum_{n=0}^{60}(4 n+7)$ $\newline$ 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=0}^{60}(4 n+7)

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Answer:

Calculate number of terms: We need to find the sum of the arithmetic series given by the formula $(4n+7)$ from $n=0$ to $n=60$ . 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.
Find first term: First, we calculate the number of terms in the series. Since the series starts at $n=0$ and ends at $n=60$ , there are $60 - 0 + 1 = 61$ terms.
Find last term: Next, we find the first term of the series by substituting $n=0$ into the formula $(4n+7)$ . This gives us $a_1 = 4(0) + 7 = 7$ .
Use sum formula: Now, we find the last term of the series by substituting $n=60$ into the formula $(4n+7)$ . This gives us $a_n = 4(60) + 7 = 240 + 7 = 247$ .
Perform calculation: We can now use the sum formula for an arithmetic series: $S = \frac{n}{2}(a_1 + a_n)$ . Substituting the values we have, $S = \frac{61}{2}(7 + 247)$ .
Multiply terms: Perform the calculation inside the parentheses first: $7 + 247 = 254$ .
Find sum: Now, multiply the number of terms by the sum of the first and last term: $S = (\frac{61}{2}) \times 254$ .
Find sum: Now, multiply the number of terms by the sum of the first and last term: $S = \frac{61}{2} \times 254$ .Perform the multiplication to find the sum of the series: $S = 61 \times 127 = 7747$ .