Final answer:
The fifth term in the expansion of the binomial (x-2¹) is the term T5, which can be found using the binomial theorem. This fifth term involves calculating C(n, 4), the combination of n items taken 4 at a time, and multiplying it by x raised to the power of (n-4) and (-2)² raised to the power of 2.
Step-by-step explanation:
The student has asked to find the fifth term in the expansion of the binomial (x-2²). To solve this, we can use the binomial theorem or Pascal's triangle. The general form for the nth term in the expansion of (a+b)^n is given by:
Tk+1 = C(n, k) · an-k · bk
Here, a = x, b = -2², and n is still unknown. We are looking for the 5th term, so k = 4 (since we start counting from 0).
The associated coefficient can be found using the factorial notation for combinations as:
- C(n, 4) = n! / (4!(n-4)!)
The fifth term can then be calculated as:
- T5 = C(n, 4) · xn-4 · (-2)2²
- T5 = C(n, 4) · xn-4 · 16
Assuming we have an expansion of the power n, the coefficient C(n, 4) will need to be computed based on the value of n.