Questions: What is a formula for the nth term of the given sequence? -12,-16,-20 ...

Solution Steps

To find the formula for the nth term of the given sequence, we need to identify the pattern in the sequence. The sequence is arithmetic with a common difference of -4. We can use the formula for the nth term of an arithmetic sequence, which is given by:

\[ a_n = a_1 + (n-1)d \]

where \( a_1 \) is the first term and \( d \) is the common difference.

The given sequence is \(-12, -16, -20, \ldots\). We observe that the sequence is arithmetic with a common difference \(d = -4\).

The formula for the nth term of an arithmetic sequence is: \[ a_n = a_1 + (n-1)d \] where \(a_1\) is the first term and \(d\) is the common difference.

Given \(a_1 = -12\) and \(d = -4\), we substitute these values into the formula: \[ a_n = -12 + (n-1)(-4) \]

Simplify the expression to find the nth term: \[ a_n = -12 - 4(n-1) \] \[ a_n = -12 - 4n + 4 \] \[ a_n = -8 - 4n \]

To verify, we calculate the 5th term using the formula: \[ a_5 = -8 - 4(5) = -8 - 20 = -28 \]

Final Answer