Answer:
a. T1 = -4 , T2 = -4/3 , T3 = -4/9 , T4 = -4/27
b. It is converge
c. The sum to ∞ = -6
Step-by-step explanation:
a.
∵ Tn = -4(1/3)^(n-1)
∵ The lower n = 1
∵ The geometric series Tn = a(r)^(n-1)
∴ T1 = a , T2 = ar , T3 = ar² , T4 = ar³
∴ a = -4 , r = 1/3
∴ T1 = -4
∴ T2 = -4(1/3) = -4/3
∴ T3 = -4(1/3)² = -4/9
∴ T4 = -4(1/3)³ = -4/27
b.
r = 1/3
∴ -1 < r < 1
∴ It is converge because the value of 1/3 when n is a very large
number will approach to zero
c.
∵ The sum of the geometric series = a(1-(r)^n)/1-r
∵ r^n ≅ 0 when n is a very large number
∴ The sum to ∞ = a/1 - r = -4/(1 - 1/3) = -4/(2/3) = -6
The smallest amount of sporting goods were sold on Sunday, baseballs to footballs. Answer: A.
This = one 1/2 circle with radius 2 in and one with radius 1
= 2pi + pi = 3pi = 9.42 in to nearest hundredth
The total change in the amount of water in the pool is 288 gallons.
<h3>What is Volume?</h3>
Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Here, Rate of water pumped into her pool = 6 gallons / minute.
Total Duration = 48 minutes
Total amount of water = Rate X Time
= 6 X 48
= 288 gallons
Thus, the total change in the amount of water in the pool is 288 gallons.
Learn more about Volume from:
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<span>B. −12, 0, 13,|−14|,|−16|, 17</span>