The question states that we need to determine the formula of the sequence. There are generally three types of sequences:
- Arithmetic: Common Difference
- Geometric: Common Ratio
- Quadratic: Second Difference
We need to determine the type of sequence before we can determine the formula of the aforementioned sequence.
The sequence was given as: √(5/4), √(3/2), √(7/4).
We need to change the sequence into decimal form as it is difficult to find the pattern in the fraction form.
The sequence in decimal form: √1.25, √1.5, √1.75
If we ignore the root we have: 1.25, 1.5, 1.75
From above we can see a clear between and that there is a common difference of 0.25
Since there is a common difference we have identified the sequence to be arithmetic.
The formula for an arithmetic sequence is as follows:
Tn = a + d*(n-1)
where
Tn: Term value
a: first term
n: Term number
So the formula of the sequence is as follows
The first term is a = 1.25, d = 0.25 and do not forget the foot:
Tn = √[1.25 + 0.25 (n-1)]
Now we know the sequence of our pattern, let double check our formula
T1=√[1.25 + 0.25 (1-1)]= √1.25 = √(5/4)
T2 = √[1.25 +0.25(2-1)] = √1.5 = √(3/2)
T3 = √[1.25 +0.25 (3-1)] = √1.75= √(7/4)
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