the second and fifth terms of an arithmetic sequence are 5 and 38 respectively. Find the explicit formula for the sequence

38-5 = 33 = 3d, so d=11

a+d = 5, so a = -6

An = -6 + (n-1)*11 = -17+11n

To find the explicit formula for an arithmetic sequence, we need to determine the common difference (d) and the first term (a).

In this case, we are given the second term (5) and the fifth term (38). We can use these two terms to find the common difference.

The formula to calculate the common difference (d) in an arithmetic sequence is:

d = (term2 - term1) / (index2 - index1)

Using the given values:
term1 = 5
index1 = 2
term2 = 38
index2 = 5

d = (38 - 5) / (5 - 2)
d = 33 / 3
d = 11

Now that we have the common difference, we can find the first term (a) using the following formula:

a = term1 - ((index1 - 1) * d)

Using the given values:
term1 = 5
index1 = 2
d = 11

a = 5 - ((2 - 1) * 11)
a = 5 - (1 * 11)
a = 5 - 11
a = -6

Therefore, the explicit formula for the arithmetic sequence is:

An = -6 + (n - 1) * 11

Where 'n' represents the index of the term in the sequence.