What is the formula for the nth term of the following sequence 1, 4, 9, 16?

The given sequence is 1, 4, 9, 16. To find the formula for the nth term, we first observe the pattern of the numbers. These numbers are perfect squares:

• 1 is 1^2
• 4 is 2^2
• 9 is 3^2
• 16 is 4^2

From this, we can deduce that the nth term of the sequence can be expressed as:

n^th term = n²

Thus, for any integer n, the nth term will be the square of n. For example:

• When n = 1, the term is 1² = 1
• When n = 2, the term is 2² = 4
• When n = 3, the term is 3² = 9
• When n = 4, the term is 4² = 16

In conclusion, the formula for the nth term of the sequence is n².