Answer:
312 yoyos in 8th week; 3407 yoyos over 8 weeks
Step-by-step explanation:
The <em>formula for the nth term</em> 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 <em>the sum of the first n terms</em> 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.
