find the number of terms in an arithmetic sequence with first term 6, common difference 2 and sum of 126
You can use the formula for the sum of an arithmetic series to find the number of terms (\(n\)):
\[ S = \frac{n}{2}[2a + (n-1)d] \]
where:
- \(S\) is the sum of the series,
- \(a\) is the first term,
- \(d\) is the common difference,
- \(n\) is the number of terms.
Given \(a = 6\), \(d = 2\), and \(S = 126\), you can plug in these values and solve for \(n\):
\[ 126 = \frac{n}{2}[2(6) + (n-1)(2)] \]
Solve this equation to find the value of \(n\).