# 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 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 .

Q21:

Find in the expansion of .

• A
• B
• C
• D
• E

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