Hello people! I am quite confused, I'm supposed to find the nth term formula for a sequence but I can't seem to figure it out. I'm hoping someone can shed light on what to do!
1/3, -2/9, 4/27, -8/81
I know that the denominator is 3^n but the numerator completely stumps me!
All you need is to find the "common ratio" by dividing the 2nd term by the 1st term: (-2/9) / (1/3) = - 2/3. Then, all you do is multiply -2/3 x 2nd term(-2/9) =4/27, which is your 3rd term. Then multiply it by - 2/3 and you get: 4/27 x - 2/3 =- 8/81, which is your 4th term..............and so on.
So, the nth term "closed form" would be:a(n) =a(n - 1) * - 2/3
So, the 5th term is:a(5) =a(5 - 1) =a(4) * - 2/3 =16 / 243........and so on.