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The sales of a company in five years were 1500, 1650, 1815, 1996. 5, and 2196. 15 units. What is the expected sales in the seventh year?
2420. 25
2560. 35
2657. 34
2880. 74
2657. 34
Identify the growth factor by dividing any term by its predecessor: 1650/1500 = 1.1. Apply this 10 percent increase factor consistently to find future terms.
Identify the growth factor by dividing any term by its predecessor: 1650/1500 = 1.1. Apply this 10 percent increase factor consistently to find future terms.
Calculate the common ratio
Divide consecutive terms: 1650 / 1500 = 1.1, 1815 / 1650 = 1.1, 1996.5 / 1815 = 1.1, and 2196.15 / 1996.5 = 1.1. The series follows a geometric progression with a common ratio of 1.1.
Calculate the 6th year sales
Multiply the 5th year value by 1.1: 2196.15 * 1.1 = 2415.765.
Calculate the 7th year sales
Multiply the 6th year value by 1.1: 2415.765 * 1.1 = 2657.3415, which rounds to 2657.34.
A: 2420.25 is incorrect as it results from misapplying the ratio to an intermediate step; B: 2560.35 does not follow the 1.1 multiplier sequence; D: 2880.74 is an arbitrary value that ignores the established growth pattern.
C is correct because the series increases by a fixed ratio of 1.1 (10 percent) each year, leading to the 7th year value of 2657.34.
When terms in a series increase by small, varying decimals, always check the ratio of the second term to the first; it often reveals a simple percentage increment.
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