What is the 24th term of the arithmetic sequence where a1 = 8 and a9 = 56?

To find the 24th term of the arithmetic sequence, we first need to determine the common difference.

We know the first term (a₁) is 8 and the ninth term (a₉) is 56.

The formula for the nth term of an arithmetic sequence is given by:

a_n = a₁ + (n – 1) * d

Here, d is the common difference. For the ninth term, we can plug in the values:

a₉ = a₁ + (9 – 1) * d

This translates to:

56 = 8 + 8d

Now, we can solve for d:

56 – 8 = 8d

48 = 8d

d = 6

Now that we have the common difference, we can find the 24th term:

a₂₄ = a₁ + (24 – 1) * d

Substituting the known values, we get:

a₂₄ = 8 + 23 * 6

a₂₄ = 8 + 138

a₂₄ = 146

Therefore, the 24th term of the arithmetic sequence is 146.