Question

The first and last terms of a 10-term arithmetic series are listed in the table. What is the sum of the series? (2 points) Term Number Term 1 3 10 75

Answer 1

Answer and Step-by-step explanation:

The arithmetic sequence general formula is an = a1 + d *(n-1) where d is the arithmetic difference and n is an integer. In this case, upon derivation, the formula that represents the sum of the series is S = (a1 + an)*(n/2). Substituting, S = (3+75)*(10/2) equal to 390

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b. 390

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Answer 2

To find the sum of an arithmetic series, we can use the formula:

Sum = (n/2) * (2a + (n-1)d)

where:

- n is the number of terms in the series

- a is the first term of the series

- d is the common difference between the terms

In this case, we are given the first term (a = 3) and the last term (term 10 = 75).

To find the common difference (d), we can use the formula:

d = (last term - first term) / (number of terms - 1)

Substituting the given values into the formula, we have:

d = (75 - 3) / (10 - 1)

d = 72 / 9

d = 8

Now, we can find the sum using the formula:

Sum = (n/2) * (2a + (n-1)d)

Substituting the values:

n = 10

a = 3

d = 8

Sum = (10/2) * (2*3 + (10-1)*8)

Sum = 5 * (6 + 9*8)

Sum = 5 * (6 + 72)

Sum = 5 * 78

Sum = 390

Therefore, the sum of the arithmetic series is 390.