find a formula for the general term a_n
{3/16,4/25,5/36,6/49}
{1/2,1/4,1/8,1/16}
Is it not n/(n+1)^2 and 1/2^n?

Question

find a formula for the general term a_n
{3/16,4/25,5/36,6/49}
{1/2,1/4,1/8,1/16}
Is it not n/(n+1)^2 and 1/2^n?

whpalmer4 · Answer

Certainly looks those are the formulas

anonymous · Answer

well its wrong and it doesn't tell me which one is wrong

mathstudent55 · Answer

Try (n + 2)/(n + 3)^2 for the first one

whpalmer4 · Answer

maybe the first one is wrong in that it doesn't start with 1/4

anonymous · Answer

These are two different sequences, right?  For the first one, it looks like the numerators are just the counting numbers, starting at 3.
The denominators are just the squares of the counting numbers, starting at 4.

mathstudent55 · Answer

The second one is ok

anonymous · Answer

its correct thanks. is there a way to find the formula or do you just kind of look at it and figure it out?

whpalmer4 · Answer

you correctly figured out the pattern, just didn't get the starting conditions right

anonymous · Answer

right i thought 3/16 was the third term

anonymous · Answer

but for more complicated problems is there a formula to figure out the formula like the easier common multiplier ones?

mathstudent55 · Answer

You were on the right track, but you just have to account for the first term of the first sequence being 3/16, when n sarts at 1. To get 3 in the numerator, you need n + 2. For the denominator, you need (n + 3)^2 since the first denominator was 16 = 4^2.

whpalmer4 · Answer

I was looking at it as find the pattern in the numbers, didn't give any thought to the initial conditions.  sloppy.

anonymous · Answer

Yes I also assumed 3/16 was the 3rd term since they didn't say anything.