HELP ME

Ah....I see now.....I misread this one........!!!!!

We can solve this in this manner

n(n -1)  = 210

n^2 - n  = 210     subtract 210 from both sides

n^2 - n - 210  = 0     factor

(n  - 15) ( n + 14) =  0

So either   .....n = 15   or n = -14   

The second doesn't make sense.....so   the 15th term is 210

There......that's better.....!!!!

BTW....Guest 1 completed the square......that's OK, but it's more work than necessary, here  !!!!

Solve for n:
n (n-1) = 210

Expand out terms of the left hand side:
n^2-n = 210

Add 1/4 to both sides:
n^2-n+1/4 = 841/4

Write the left hand side as a square:
(n-1/2)^2 = 841/4

Take the square root of both sides:
n-1/2 = 29/2 or n-1/2 = -29/2

Add 1/2 to both sides:
n = 15 or n-1/2 = -29/2

Add 1/2 to both sides:
Answer: | n = 15 or n = -14

THIS IS THE 15TH TERM UNDER YOUR RULE.

The 210th term is given by :

210 (210 - 1) =

210 (209)  = 43890

BTW....this is just the sum of the first 209 positive/even integers....

CPhill: Isn't the question: what term IS 210?

if the rule is n(n-1) what term is 210

0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272............etc  

The 15th term.