Question

I need to find the fifth term of these sequences.

10. (x^2 - 1/2)^9

12. (x^2 + 2y)^8

Answer 1

I don't need the answer given to me. I want to know what i need to do to find the fifth term. If I turn the x to a five in the first sequence I get a pretty ridiculously high number that I am pretty sure isn't the answer.

Answer 2

Use Pascal's triangle. The 5th term on the nth row is

C(n,4) a^(n-4)b^4

so, for (x^2 - 1/2)^9
the 5th term is

C(9,4)(x^2)^5(-1/2)^4 = 63/8 x^10

work the other in like wise.