What is the value of the fourth term in a geometric sequence for which a1 = 30 and r = 12?

To find the fourth term in a geometric sequence, we can use the formula for the nth term of a geometric sequence, which is given by:

a_n = a₁ * r^(n-1)

Here:

• a₁ is the first term of the sequence,
• r is the common ratio,
• n is the term number.

In this case, we know

• a₁ = 30,
• r = 12,
• and we want to find a₄ (the fourth term).

Plugging these values into the formula:

a₄ = 30 * 12^(4-1)

Calculating further:

a₄ = 30 * 12³

Now calculating 12³:

12³ = 12 * 12 * 12 = 1728

So, substituting back, we have:

a₄ = 30 * 1728

Now we can do the multiplication:

a₄ = 51840

Therefore, the value of the fourth term in the geometric sequence is 51840.