What is the sixth term of the arithmetic sequence if the 10th term is 33 and the 15th term is 53.

there are 5 terms between T10 and T15, so d=20/5 = 4

T6 = T10 - 4d = 33-16 = 17

To find the sixth term of an arithmetic sequence, we need to determine the common difference (d) and use the formula for the nth term.

First, we can find the common difference (d) by subtracting the 10th term from the 15th term:

d = 15th term - 10th term
d = 53 - 33
d = 20

Now that we have the common difference, we can use the formula for the nth term of an arithmetic sequence:

nth term = a + (n - 1) * d

where a is the first term, n is the term number, and d is the common difference.

To find the 6th term, we substitute a = ?, n = 6, and d = 20 into the formula:

6th term = ? + (6 - 1) * 20
6th term = ? + 5 * 20
6th term = ? + 100

Since we don't have the value of the first term (a), we can't determine the exact value of the 6th term.

To find the sixth term of the arithmetic sequence, we need to first find the common difference (d). We can obtain the common difference using the formula:

d = (15th term - 10th term) / (15 - 10)

Substituting the given values:

d = (53 - 33) / 5
d = 20 / 5
d = 4

Now that we have the common difference, we can find the sixth term using the formula:

nth term = a + (n - 1)d

Substituting the values for the 10th term (a) and the common difference (d):

6th term = 33 + (6 - 1) * 4
6th term = 33 + 5 * 4
6th term = 33 + 20
6th term = 53

Therefore, the sixth term of the arithmetic sequence is 53.