The sum, \(S_{n}\), of a sequence is given by \(S_{n} = 2n^{2} - 5\). Find the 6th term.
Answer Details
To find the 6th term of the sequence, we need to find the difference between the sum of the first 6 terms and the sum of the first 5 terms. The sum of the first 5 terms is:
$S_5 = 2(5)^2 - 5 = 45$
The sum of the first 6 terms is:
$S_6 = 2(6)^2 - 5 = 67$
Therefore, the 6th term of the sequence is:
$S_6 - S_5 = 67 - 45 = 22$
So the answer is 22.