Find an equation for the nth term of the sequence 4, 16, 64, 256

To find the equation for the nth term of the sequence 4, 16, 64, 256, we first observe the pattern in the sequence.

The terms can be rewritten as:

• 4 = 4¹
• 16 = 4²
• 64 = 4³
• 256 = 4⁴

From this, we can see that each term is a power of 4. In general, the nth term can be expressed as:

a_n = 4ⁿ

where a_n is the nth term of the sequence. Therefore, to find the term corresponding to n = 1, 2, 3, and 4, we simply substitute the values of n into the formula:

• If n = 1, a₁ = 4¹ = 4
• If n = 2, a₂ = 4² = 16
• If n = 3, a₃ = 4³ = 64
• If n = 4, a₄ = 4⁴ = 256

This confirms our formula, as it generates the correct sequence. In conclusion, the nth term of the sequence is given by a_n = 4ⁿ.