## Consider this sequence:4, 11, 18, 25, . . .What is the explicit function that defines this sequence? If arithmetic, write the function in simplified form. If geometric, write the function with an exponent of n − 1.

### To determine the explicit function that defines the given sequence, we need to observe the pattern and determine if it is arithmetic or geometric

To determine the explicit function that defines the given sequence, we need to observe the pattern and determine if it is arithmetic or geometric.

From the given sequence: 4, 11, 18, 25, …

If we subtract each consecutive term, we can observe that the common difference between terms is 7. Hence, we can conclude that this sequence is an arithmetic sequence.

For an arithmetic sequence, the explicit formula is given by:

an = a1 + (n-1)d

where:

an = the nth term of the sequence

a1 = the first term of the sequence

d = the common difference between terms

n = the position of the term in the sequence

In our case, the first term a1 is 4, and the common difference d is 7.

Therefore, the explicit function that defines this sequence is:

an = 4 + 7(n – 1)

Simplifying the expression further:

an = 4 + 7n – 7

an = 7n – 3

So, the explicit function for this arithmetic sequence is an = 7n – 3.

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