The formula that describes the sequence is 
Step-by-step explanation:
The nth-term formula for a geometric sequence is 
, where
- a represents the first term of the sequence
- r signifies the common ratio between any two consecutive terms
= 
∵ The sequence is 
, -4, -24, -144,.......
∵ The first term is
∵ The second term is -4
∴ 
∵ The third term is -24
∴ 
∵ The fourth term is -144
∴ 
∵ 
= = 
= 6
∴ There is a consistent ratio between two consecutive terms
∴ The sequence qualifies as a geometric sequence
∵ The formula for the nth term of the geometric sequence is
∵ a =
∵ r = 6
∴ The equation for the sequence is
The formula that can be employed to outline the sequence is
Learn more:
You can explore more about sequences in
Multiplying 3 × 5 × 2 × 4 × 3 × 2 × 1 × 1 results in 720
Hello! You need to calculate a 99% confidence interval for the difference in mean lifespan between two tire brands. Each tested car was assigned one tire from each brand randomly on the rear wheels, allowing for paired sample analysis.
Brand 1 Brand 2 X₁-X₂
car 1: 36,925; 34,318; 2.607
car 2: 45,300; 42,280; 3.020
car 3: 36,240; 35,500; 0.740
car 4: 32,100; 31,950; 0.150
car 5: 37,210; 38,015; -0.0805
car 6: 48,360; 47,800; 1.160
car 7: 38,200; 37,810; 0.390
car 8: 33,500; 33,215; 0.285
n= 8
The study variable is defined as Xd= X₁-X₂, where X₁ represents the tire lifespan (in km) from Brand 1 and X₂ represents Brand 2. Thus, Xd is the difference in tire lifespan.
Xd~N(μd;δd²) (normality test p-value is 0.4640).
For calculating the confidence interval, the best statistic is the Student's t using the following formula:
t= (xd[bar] - μd)/(Sd/√n) ~t₍ₙ₋₁₎
sample mean: xd[bar]= 0.94
standard deviation: Sd= 1.29
= 3.355
xd[bar] ±
*(Sd/√n) ⇒ 0.94 ± 3.355*(1.29/√8)
[-0.65;2.54]km.
The CI can be compared to bilateral hypothesis testing:
H₀:μd=0
H₁:μd≠0
using significance level of 0.01.
Since the confidence interval includes zero, we do not reject the null hypothesis, indicating no significant difference between the tire brands.
Hope you have a fantastic day!
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