Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues

general-term

#1

find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. Note all fractions have been simplified. {-1/4, 2/3, -9/8, 8/5, -25/12,…}

Answer:

So first, let’s make all the denominators even…
-1/4 , 4/6 , -9/8 , 16/10, -25/12
Each denominator is the square of it’s x value (number in the sequence)
and each numerator is -1^x * x^2
[(-1)^x) x^2]/(2(x+1))