Find the sum of the first 10 terms of the arithmetic sequence where the first term is 5 and the common difference is 3.

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Step:1 ：The formula for the sum of the first n terms of an arithmetic sequence is given by (S_n = frac{n}{2}(a_{1} + a_{n})) where (a_{1}) is the first term, (a_{n}) is the nth term, and n is the number of terms.Step:2 ：In this case, (a_{1} = 5), (d = 3), and (n = 10). The nth term of an arithmetic sequence is given by (a_{n} = a_{1} + (n - 1)d). Thus, (a_{10} = 5 + (10 - 1)3 = 32).Step:3 ：Substituting these into the formula gives (S_{10} = frac{10}{2}(5 + 32) = 185).

Answer

Step: 1 ：The formula for the sum of the first n terms of an arithmetic sequence is given by (S_n = frac{n}{2}(a_{1} + a_{n})) where (a_{1}) is the first term, (a_{n}) is the nth term, and n is the number of terms.Step: 2 ：In this case, (a_{1} = 5), (d = 3), and (n = 10). The nth term of an arithmetic sequence is given by (a_{n} = a_{1} + (n - 1)d). Thus, (a_{10} = 5 + (10 - 1)3 = 32).Step: 3 ：Substituting these into the formula gives (S_{10} = frac{10}{2}(5 + 32) = 185).

Find the sum of the first 10 terms of the arithmetic sequence where the first term is 5 and the common difference is 3.

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