Question

can you please cancer C what is the explicit function and the relationships for the term please I dont understand

Answer 1

EXPLANATION

Given the sequence:

C. 3, 12, 27, 48, 75

First, we need to calculate the difference between terms:

12-3 = 9 27-12 = 15 48-27 = 21 75 - 28 = 27

Arithmetic relationship: 9, 15 , 21, 27

To obtain the sequence we use the following formula:

`a_n=a_1+(n-1)d`

Now, we need to calculate the appropriate difference between terms:

15-9 = 6 21-25 = 6 27 - 21 = 6

So the constant difference is 6 and the nth term will be:

nth = 6n + 3

*a1=3

So, the relationship will be:

n Value Relationship

1 12 3 + (6*1 +3)

2 27 12 + (6*2 + 3)

3 48 27 + (6*3 + 3)

4 75 48 + (6*4 + 3)

5 108 75 + (6*5 + 3)

n n-1 + (6n+3) n-1 + (6n+3)

Explicit function: y = (n-1) + (6n+3)