Find the number of terms in the sequence or the sum of the sequence as requested.
-Find the sum of the following arithmetic sequence. 10 + 11 + 12 + . . . + 500
A)125,205
B)124,714
C)125,250
D)125,214

Question

Quizplus · Accepted Answer

The sum of an arithmetic sequence can be found using the formula:Sum = (n/2) * (a1 + an)where n is the number of terms, a1 is the first term, and an is the last term.In this case, a1 = 10, an = 500, and n is unknown. We can find n by using the formula:n = (an - a1) / d + 1where d is the common difference. In this case, d = 1.Substituting these values into the formula, we get:n = (500 - 10) / 1 + 1 = 491Now we can find the sum using the formula:Sum = (n/2) * (a1 + an) = (491/2) * (10 + 500) = 125,205Therefore, the sum of the sequence is 125,205.

Find the Number of Terms in the Sequence or the Sum