15
QuizMultiple Choice

Arithmetic Series — Quiz

Question 15 • Precalculus

The manager of a store is stacking boxes for a display. There are 18 boxes on the bottom row. Each successive row has one less box than the previous row. The expression the sum from n is equal to 1 to 15 of open bracket 18 minus open paren n minus 1 close paren close bracket represents the total number of boxes in the display for the first 15 rows. How many boxes are in the display?

Answer
A
165
B
330
C
22
D
18

Explanation

The rows contain 18, 17, 16, and so on, decreasing by 1 each time. After 15 rows, the last row has 18 − 14 = 4 boxes. The total is the sum of 15 terms from 18 to 4: (18 + 4) × 15 ÷ 2 = 165 boxes, so the correct choice is A, 165.

AI-written and checked against the verified answer.

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