# Worksheet: General Term in the Binomial Theorem

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.

**Q1: **

Find in the expansion of .

- A
- B
- C
- D
- E

**Q2: **

Find the coefficient of in the expansion of .

**Q3: **

Find in the expansion of .

- A
- B
- C
- D

**Q4: **

Find in the expansion of .

- A
- B
- C
- D

**Q5: **

Find the third term in the expansion of .

- A
- B
- C
- D

**Q6: **

Consider the binomial expansion of in ascending powers of . What is the seventh term?

- A
- B
- C
- D

**Q7: **

Find the general term in .

- A
- B
- C
- D
- E

**Q8: **

Find in the expansion of .

- A
- B
- C
- D
- E

**Q9: **

Find the third term in the expansion of .

- A
- B
- C
- D

**Q10: **

In a binomial expansion, where the general term is , determine the position of the term containing .

- A
- B
- C
- D

**Q11: **

Let be the term in the expansion of in increasing powers of . Find all nonzero values of for which .

- A2, 14
- B2, 1
- C2,
- D4, 12

**Q12: **

Find the second-to-last term in .

- A
- B
- C
- D

**Q13: **

If the ratio between the fourth term in the expansion of and the third term in the expansion of equals , find the value of .

- A
- B
- C
- D

**Q14: **

Consider the binomial expansion of in ascending powers of . Given that when , find the value of .

**Q15: **

Given that the sum of the first, middle, and last terms in the expansion of is 42,337, find all possible real values of .

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

**Q16: **

Let be the th term in the expansion of in descending powers of . Find all the nonzero values of for which .

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

**Q17: **

Consider the expansion of in ascending powers of . Given that the coefficient of is equal to the coefficient of , determine the value of .

**Q18: **

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

- A
- B
- C
- D

**Q19: **

In the binomial expansion of , is a positive, whole number and is the th term, or the term which contains .

If , what is the value of ?

**Q20: **

Consider the expansion of . Find the values of given that the coefficient of is equal to the coefficient of .

**Q21: **

If is the term free of in , find .

**Q22: **

Find in the expansion of .

- A
- B
- C
- D
- E

**Q23: **

Find in the expansion of .

- A
- B
- C
- D
- E

**Q24: **

Find the coefficient of in the expansion of .

**Q25: **

Answer the following questions for the expansion of .

Given that the coefficient of is 3,840, find .

- A
- B
- C
- D
- E

Hence, work out the value of the coefficient of .