Find the numerical answer to the summation given below. sum_(n=0)^(93)(3n+10) Answer:

Find First Term and Common Difference: We need to find the sum of the arithmetic series where the first term a_1 is when n=0, which gives us 3(0) + 10 = 10, and the common difference d is the coefficient of n, which is 3. The number of terms in the series is 93 + 1, because we start counting from n=0.Calculate Last Term: The last term a_93 is when n=93, which gives us 3(93) + 10 = 279 + 10 = 289.Use Arithmetic Series Formula: The sum of an arithmetic series can be found using the formula S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, a_n is the last term, and n is the number of terms.Calculate Sum of Series: Plugging the values into the formula, we get S_94 = 94/2 * (10 + 289) = 47 * (299).Calculating the sum, we get S_94 = 47 * 299 = 14053.

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

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\sum_{n=0}^{93}(3 n+10)

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Answer:

Find First Term and Common Difference: We need to find the sum of the arithmetic series where the first term $a_1$ is when $n=0$ , which gives us $3(0) + 10 = 10$ , and the common difference $d$ is the coefficient of $n$ , which is $3$ . The number of terms in the series is $93 + 1$ , because we start counting from $n=0$ .
Calculate Last Term: The last term $a_{93}$ is when $n=93$ , which gives us $3(93) + 10 = 279 + 10 = 289$ .
Use Arithmetic Series Formula: The sum of an arithmetic series can be found using the formula $S_n = \frac{n}{2} \times (a_1 + a_n)$ , where $S_n$ is the sum of the first $n$ terms, $a_1$ is the first term, $a_n$ is the last term, and $n$ is the number of terms.
Calculate Sum of Series: Plugging the values into the formula, we get $S_{94} = \frac{94}{2} \times (10 + 289) = 47 \times (299)$ .
Calculate Sum of Series: Plugging the values into the formula, we get $S_{94} = \frac{94}{2} \times (10 + 289) = 47 \times (299)$ .Calculating the sum, we get $S_{94} = 47 \times 299 = 14053$ .