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.
Q2:
Find in the expansion of .
- A
- B
- C
- D
Q3:
Find in the expansion of .
- A
- B
- C
- D
Q4:
Find the third term in the expansion of .
- A
- B
- C
- D
Q5:
Consider the binomial expansion of in ascending powers of . What is the seventh term?
- A
- B
- C
- D
Q6:
Find the general term in .
- A
- B
- C
- D
- E
Q7:
Find in the expansion of .
- A
- B
- C
- D
- E
Q8:
Find the third term in the expansion of .
- A
- B
- C
- D
Q9:
In a binomial expansion, where the general term is , determine the position of the term containing .
- A
- B
- C
- D
Q10:
Let be the term in the expansion of in increasing powers of . Find all nonzero values of for which .
- A2, 1
- B4, 12
- C2,
- D2, 14
Q11:
Find the second-to-last term in .
- A
- B
- C
- D
Q12:
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
Q13:
Consider the binomial expansion of in ascending powers of . Given that when , find the value of .
Q14:
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,
Q15:
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,
Q16:
Consider the expansion of in ascending powers of . Given that the coefficient of is equal to the coefficient of , determine the value of .
Q17:
If the coefficient of the third term in the expansion of is , determine the middle term in the expansion.
- A
- B
- C
- D
Q18:
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 ?
Q19:
Consider the expansion of . Find the values of given that the coefficient of is equal to the coefficient of .
Q20:
If is the term free of in , find .
Q22:
Find in the expansion of .
- A
- B
- C
- D
- E
Q23:
Find the coefficient of in the expansion of .
Q24:
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 .
Q25:
For which values of are the two middle terms of equal?
- A
- B
- C
- D