Suppose that a new company that makes yo yos made 560 yoyos the first week the company overestimated its requirements. The managements intends to decrease the number of yoyo how the company will manufacture by 8 percent each week for 8 week.

The number of yo-you that the company can be represented by a geometric sequence

How many yo-yos will the company manufacture in 8 weeks?

312 yoyos in 8th week; 3407 yoyos over 8 weeks

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 560 and r = 0.92.

Thus, the formula for your sequence is

aₙ = 560 (0.92) ⁿ⁻¹

Eighth term

a₈ = 560 (0.92) ⁷ = 560 * 0.5578 = 312

The company will manufacture 312 yoyos in the eighth week.

Sum over eight weeks

The formula for the sum of the first n terms of a geometric series is

Sum = a₁[ (1 - rⁿ) (1 - r) ]

Sum = 560[ (1 - 0.92⁸) / (1 - 092) ]

= 560[ (1 - 0.513 22) / 0.08 ]

= 560 * (0.486 78/0.08)

= 560 * 6.0848

= 3407

The company will manufacture a total of 3407 yoyos over eight weeks.