Answer:
To find the 13th term of the arithmetic series, we need to use the formula for the sum of the first n terms:
Sn = n/2 * (a1 + an)
where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.
We are given that Sn = n² - 2n. To find an expression for the nth term, we can use the formula for the sum of an arithmetic series:
Sn = n/2 * (a1 + an)
n² - 2n = n/2 * (a1 + an)
Simplifying and rearranging:
an = n/2 * (a1 + an) - n² + 2n
an - n/2 * an = n/2 * a1 - n² + 2n
(1 - n/2) * an = n/2 * a1 - n² + 2n
an = (n/2) * (2a1 - n + 2)
Now we can substitute n=13 to find the 13th term:
a13 = (13/2) * (2a1 - 13 + 2)
a13 = 6.5 * (2a1 - 11)
We cannot determine a13 without knowing the value of a1.
Explanation: