The sum of the first 10 terms of an arithmetic sequence is given by S_n = n/2 (2a1 + (n-1)d). Find the sum of the first 10 terms when a1 = 4 and d = 3.

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Multiple Choice

The sum of the first 10 terms of an arithmetic sequence is given by S_n = n/2 (2a1 + (n-1)d). Find the sum of the first 10 terms when a1 = 4 and d = 3.

Explanation:
Sum of terms in an arithmetic sequence can be found using the formula S_n = n/2 [2a1 + (n-1)d], which essentially averages the start and end terms across all terms. With ten terms, a1 = 4 and d = 3, compute S_10 as 10/2 [2*4 + (10-1)*3] = 5 [8 + 27] = 5 * 35 = 175. You can also check by finding the last term: a_n = a1 + (n-1)d = 4 + 9*3 = 31, then S_10 = 10*(a1 + a_n)/2 = 10*(4 + 31)/2 = 175. So the sum is 175.

Sum of terms in an arithmetic sequence can be found using the formula S_n = n/2 [2a1 + (n-1)d], which essentially averages the start and end terms across all terms. With ten terms, a1 = 4 and d = 3, compute S_10 as 10/2 [24 + (10-1)3] = 5 [8 + 27] = 5 * 35 = 175. You can also check by finding the last term: a_n = a1 + (n-1)d = 4 + 93 = 31, then S_10 = 10(a1 + a_n)/2 = 10*(4 + 31)/2 = 175. So the sum is 175.

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