Find the numerical answer to the summation given below. sum_(n=0)^(85)(2n+5) Answer:

Find First Term: We need to find the sum of the arithmetic series where the nth term is given by the formula $ a_n = 2n + 5 $. The series starts at $ n = 0 $ and ends at $ n = 85 $.Find Last Term: First, let's find the first term of the series ($ a_1 $) when $ n = 0 $. We substitute $ n = 0 $ into the formula to get $ a_1 = 2(0) + 5 = 5 $.Use Sum Formula: Next, we find the last term of the series ($ a_{86} $) when $ n = 85 $. We substitute $ n = 85 $ into the formula to get $ a_{86} = 2(85) + 5 = 170 + 5 = 175 $.Apply Formula: 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. In this case, there are $ 86 $ terms because we start counting from $ n = 0 $.Simplify Expression: Now we apply the formula to find the sum of the series: $ S = \frac{86}{2}(5 + 175) $.Calculate Sum: Simplify the expression inside the parentheses: $ S = \frac{86}{2}(180) $.Perform Multiplication: Now, calculate the sum: $ S = 43 \times 180 $.Perform the multiplication to find the sum: $ S = 7740 $.

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Find the numerical answer to the summation given below.

sum_(n=0)^(85)(2n+5)
Answer:

Find the numerical answer to the summation given below. $\newline$ $\sum_{n=0}^{85}(2 n+5)$ $\newline$ 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}^{85}(2 n+5)

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Answer:

Find First Term: We need to find the sum of the arithmetic series where the nth term is given by the formula $a_n = 2n + 5$ . The series starts at $n = 0$ and ends at $n = 85$ .
Find Last Term: First, let's find the first term of the series ( $a_1$ ) when $n = 0$ . We substitute $n = 0$ into the formula to get $a_1 = 2(0) + 5 = 5$ .
Use Sum Formula: Next, we find the last term of the series ( $a_{86}$ ) when $n = 85$ . We substitute $n = 85$ into the formula to get $a_{86} = 2(85) + 5 = 170 + 5 = 175$ .
Apply Formula: 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. In this case, there are $86$ terms because we start counting from $n = 0$ .
Simplify Expression: Now we apply the formula to find the sum of the series: $S = \frac{86}{2}(5 + 175)$ .
Calculate Sum: Simplify the expression inside the parentheses: $S = \frac{86}{2}(180)$ .
Perform Multiplication: Now, calculate the sum: $S = 43 \times 180$ .
Perform Multiplication: Now, calculate the sum: $S = 43 \times 180$ .Perform the multiplication to find the sum: $S = 7740$ .