Answer:
24th term
Step-by-step explanation:
Given
[tex]S_n = 600[/tex]
[tex]Sequence:2,4,6,8..[/tex]
Required
Find n
First, calculate common difference d
[tex]d = 4 -2 = 2[/tex]
Calculate n using:
[tex]S_n = \frac{n}{2}[2a + (n - 1)d][/tex]
So:
[tex]600 = \frac{n}{2}[2*2 + (n - 1)*2][/tex]
[tex]600 = \frac{n}{2}[4 + 2n - 2][/tex]
Multiply by 2
[tex]120 = n[2 + 2n][/tex]
[tex]1200 = 2n^2 + 2n[/tex]
Rewrite as:
[tex]2n^2 + 2n - 1200 = 0[/tex]
Divide by 2
[tex]n^2 + n - 600 = 0[/tex]
Solve quadratic equation.
It gives:
[tex]n = -25\ n = 24[/tex]
Since n can't be negative;
Then
[tex]n = 24[/tex]
