We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:
The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:
Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:
Where (from tables):
Finally, the interval at 98% confidence level is:
Answer:
The Recursive formula for the sequence is:
aₙ = aₙ₋₁ + d
The Explicit formula for the sequence is:
Step-by-step explanation:
Given the sequence
3,7,11,15
Here:
a₁ = 3
computing the differences of all the adjacent terms
7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4
The difference between all the adjacent terms is the same and equal to
d = 4
We know that a recursive formula basically defines each term of a sequence using the previous term(s).
The recursive formula of the Arithmetic sequence always involves the first term.
a₁ = 3
We know that, in the Arithmetic sequence, every next term can be obtained by adding the common difference and the preceding term.
so
The recursive formula of the sequence is:
aₙ = aₙ₋₁ + d
substitute n = 2 to find the 2nd term
a₂ = a₂₋₁ + d
a₂ = a₁+ d
substitute a₁ = 3 and d = 4
a₂ = 3 + 4
a₂ = 7
Thus, the recursive formula for the sequence 3,7,11,15 is:
aₙ = aₙ₋₁ + d
<u>An explicit rule for the sequence</u>
Given the sequence
3,7,11,15
We already know that
a₁ = 3
d = 4
An arithmetic sequence has a constant difference 'd' and is defined by
substituting a₁ = 3 and d = 4
Therefore, an explicit rule for the sequence