3/2, 9/4, 3, 15/4. what is the formula for this sequence?

Question

i have a hard time with math and fractions so i  need help figuring out this sequence formula above.

Answer 1

The problem gives the values as fractions just to make it harder.  If you have a hard time with fractions, then you need to find a way to make them easier.

 

Let's consider two sequences and see if we can understand this sequence better.

This problem:         3/2,      9/4,      3,       15/4

Each times 4:          6,         9,        12,      15               [Hey! this is a lot easier to understand!]

 

So if the difference in the second sequence is always 3, then the difference in the problem sequence is always 3/4 (remember, we multiplied by 4 so now we must divide by 4 to get back)

 

This is an arithmetic sequence.  For an arithmetic sequence, the formula is:

     a_n = a + (n – 1)d

                where a = first term

                          a_n = n^th term

                          d = common difference

 

So,    a_n = (3/2) + (n-1)(3/4)

 

Let's check:

    n          a_n

   ----      -----

    1         3/2

    2         3/2 + (1)(3/4)  =  6/4 + 3/4  = 9/4

    3         3/2 + (2)(3/4)  =  6/4 + 6/4  = 12/4  =  3

    4         3/2 + (3)(3/4)  =  6/4 + 9/4  = 15/4

 

Oh, how did I decide to multiply by 4?  It is the LCD of the denominators (so they all go away).

Answer 2

When dealing with sequences, I check first for arithmetic, i.e., having a common difference.

 

9/4 - 3/4 = 3/4

3 - 9/4 = 3/4

 

a_n = (3/2) + (n - 1)(3/4)

Answer 3

9/4 - 3/2 = 3/4

 

3 - 9/4 = 3/4

 

15/4 - 3 = 3/4

 

The sequence is arithmetic with common difference d = 3/4

 

The nth term, a_n, is given by the formula a_n = a₁+(n-1)d

 

                                                         a_n = 3/2+(n-1)(3/4)

 

                                                         a_n = (3/4)n + 3/4

 

 

Answer 4

Hi Brenda!

 

So, the pattern starts like this: first, you multiply the first fraction in the sequence [3/2] by that same fraction, 3/2. When you do that, you will end up with the next term in the sequence, 9/4. From there, you simply increase both the numerator AND denominator by 1 and multiply it by the previous term to find the next term in the sequence. Since the first fraction was multiplied by 3/2, you would then multiply the next term by 4/3, and the next term by 5/4. This will give you the terms featured in this sequence.

 

Hope that helps!!