What is the 21st term in a sequence where each term is 15 times the previous term?

To find the 21st term of a sequence where every term is 15 times the previous term, we can first establish the formula for the nth term of a geometric sequence.

The general formula for the nth term of a geometric sequence is:

A_n = A₁ × r^(n-1)

Where:

• A_n is the nth term you want to find.
• A₁ is the first term of the sequence.
• r is the common ratio (the factor by which we multiply each term to get the next term).
• n is the term number.

In this case:

• The first term, A₁, can be assumed to be 1 (or any other starting value, but we typically begin with 1 for simplicity).
• The common ratio, r, is 15.
• We want to find the 21st term, so n will be 21.

Plugging these values into the formula, we get:

A₂₁ = 1 × 15^(21-1)

Which simplifies to:

A₂₁ = 1 × 15²⁰

Finally, calculate 15²⁰:

The value of 15²⁰ is a large number:

A₂₁ = 15,593,083,298,246,098,529,307,750,001

Therefore, the 21st term in the sequence where each term is 15 times the previous term is certainly a massive number, exemplifying the rapid growth typical of geometric sequences!