Question: A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is…

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

740.0

190.0

42.5

465.0

Solution

The problem states: A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number? To find the first number, we can use the formula for the sum of an arithmetic series: \[ S = \frac{n}{2} \times (a + l) \] where: - \( S \) is the sum of the series - \( n \) is the number of terms - \( a \) is the first term - \( l \) is the last term We know: - \( S = 4,185 \) - \( n = 18 \) - \( l = 275 \) Substituting these values into the formula gives: \[ 4,185 = \frac{18}{2} \times (a + 275) \] Simplify \(\frac{18}{2}\) to get 9: \[ 4,185 = 9 \times (a + 275) \] Divide both sides by 9: \[ 465 = a + 275 \] Subtract 275 from both sides to solve for \( a \): \[ a = 465 - 275 \] \[ a = 190 \] So, the first number in the series is 190.0.