I need to find the fifth term of these sequences.
10. (x^2 - 1/2)^9
12. (x^2 + 2y)^8
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.
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.
To find the fifth term of a sequence, we need to know the general formula for the nth term.
For sequence 10, the general formula for the nth term is (x^2 - 1/2)^n. To find the fifth term, we substitute n = 5 into the formula:
(5^2 - 1/2)^9
Simplifying this expression would require knowing the value of x, as it cannot be further simplified without specific values.
For sequence 12, the general formula for the nth term is (x^2 + 2y)^8. Once again, to find the fifth term, we substitute n = 5 into the formula:
(x^2 + 2y)^8
Similarly, without knowing the values of x and y, we cannot simplify this expression any further to find the fifth term.