Question

Finf the 12th term for the sequence below.
n^2-3n-6.

Answer 1

The 12th term for the sequence
`\(n^2 - 3n - 6\)` is 150.

Step-by-step explanation:

The given sequence is represented by the formula
`\(n^2 - 3n - 6\)`. To find the 12th term, substitute
`\(n = 12\)` into the formula:

`\[12^2 - 3 * 12 - 6\]`

Simplifying this expression gives the final answer of 150. This result is obtained by squaring 12, multiplying 3 by 12, and subtracting 6, following the pattern of the given sequence. Each term in the sequence is generated by substituting the corresponding value of
`\(n\)` into the formula.

In the formula
`\(n^2 - 3n - 6\), the first term (\(n^2\))`represents the square of the position in the sequence, the second term
`(\(-3n\))` represents three times the position, and the last term
`(\(-6\))` is a constant subtracted in each case. This pattern helps generate each term in the sequence. Therefore, by substituting
`\(n = 12\)` into the formula, the 12th term is found to be 150.