Find the sum. sum_(k=1)^(50)(5k-161)=

Find First Term: We need to find the sum of the arithmetic series given by the expression (5k-161) from k=1 to 50. The sum of an arithmetic series can be found using the formula S = n/2 * (a1 + an), where n is the number of terms, a1 is the first term, and an is the last term.Calculate Last Term: First, we calculate the first term of the series when k=1. The first term a1 is given by the expression (5k-161) when k=1, which is (5*1-161) = 5-161 = -156.Apply Sum Formula: Next, we calculate the last term of the series when k=50. The last term an is given by the expression (5k-161) when k=50, which is (5*50-161) = 250-161 = 89.Calculate Sum: Now we have the first term a1 = -156 and the last term an = 89. We also know the number of terms n = 50. We can now use the sum formula for an arithmetic series: S = n/2 * (a1 + an).Plugging the values into the formula, we get S = 50/2 * (-156 + 89) = 25 * (-67) = -1675.

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Find the sum. $\newline$ $\sum_{k=1}^{50}(5 k-161)=$

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. Find the sum.

\newline

\sum_{k=1}^{50}(5 k-161)=

Find First Term: We need to find the sum of the arithmetic series given by the expression $5k-161$ from $k=1$ to $50$ . The sum of an arithmetic series can be found using the formula $S = \frac{n}{2} \times (a_1 + a_n)$ , where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term.
Calculate Last Term: First, we calculate the first term of the series when $k=1$ . The first term $a_1$ is given by the expression $(5k-161)$ when $k=1$ , which is $(5\times 1-161) = 5-161 = -156$ .
Apply Sum Formula: Next, we calculate the last term of the series when $k=50$ . The last term $a_n$ is given by the expression $(5k-161)$ when $k=50$ , which is $(5\times 50-161) = 250-161 = 89$ .
Calculate Sum: Now we have the first term $a_1 = -156$ and the last term $a_n = 89$ . We also know the number of terms $n = 50$ . We can now use the sum formula for an arithmetic series: $S = \frac{n}{2} \times (a_1 + a_n)$ .
Calculate Sum: Now we have the first term $a_1 = -156$ and the last term $a_n = 89$ . We also know the number of terms $n = 50$ . We can now use the sum formula for an arithmetic series: $S = \frac{n}{2} \times (a_1 + a_n)$ . Plugging the values into the formula, we get $S = \frac{50}{2} \times (-156 + 89) = 25 \times (-67) = -1675$ .