√5/4,√3/2,√7/4. Find the formula for this sequence. √ this symbol means square root

The question states that we need to determine the formula of the sequence. There are generally three types of sequences:

1. Arithmetic: Common Difference 


2. Geometric: Common Ratio


3. 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)