# Lesson Worksheet: General Term in the Binomial Theorem Mathematics

In this worksheet, we will practice finding a specific term and the coefficient of a specific term inside a binomial expansion without the need to fully expand the series.

**Q4: **

The terms of the expansion of are arranged according to the descending powers of . Given that , find the value of .

**Q5: **

If the coefficient of the third term in the expansion of is , determine the middle term in the expansion.

- A
- B
- C
- D

**Q7: **

Consider the expansion of , where is positive. Find the values of , , and given that , , and .

- A, ,
- B, ,
- C, ,
- D, ,

**Q8: **

Consider the binomial expansion of in ascending powers of . When , one of the terms in the expansion is equal to twice its following term. Find the position of these two terms.

- A,
- B,
- C,
- D,

**Q9: **

Consider the expansion of , where is a positive constant. Determine the values of and , given that the ratio between the coefficients of and is equal to and that the ratio between the coefficients of and is equal to .

- A,
- B,
- C,
- D,