# Worksheet: Middle Term in the Binomial Theorem

Q1:

Find the middle term in the expansion of .

• A
• B
• C
• D

Q2:

Find the middle term in the expansion of .

• A
• B
• C
• D

Q3:

For which values of are the two middle terms of equal?

• A
• B
• C
• D

Q4:

Given that the middle term in the expansion of is , find .

Q5:

Consider the expansion of . Are the middle terms of the expansion equal when ?

• Ano
• Byes

Q6:

Given that the middle term in the expansion of is equal to , find the value of .

• A13
• B
• C
• D
• E

Q7:

Find the result of dividing the lower-order middle term by the higher one in the expansion of .

• A
• B
• C
• D

Q8:

In the expansion of , the two middle terms are equal when . Which of the following represents the correct relation between and ?

• A
• B
• C
• D

Q9:

Determine the value of if the value of the middle term in the expansion of is 4β320.

Q10:

Find the middle term in the expansion of .

Q11:

Consider the expansion of . Find the value of given that the middle terms of the expansion are and .

Q12:

Consider the expansion of . Find the value of given that the middle terms of the expansion are equal.

• A1
• B
• C
• D

Q13:

Consider the expansion of in descending powers of . For which values of is the sum of the two middle terms equal to zero?

• A19
• B36
• C38
• D6

Q14:

What is the middle term in the following expansion:

• A
• B
• C
• D

Q15:

Find the two middle terms in the expansion of .

• A ,
• B ,
• C ,
• D ,

Q16:

Find the two middle terms in the expansion of .

• A ,
• B ,
• C ,
• D ,

Q17:

Given that the two middle terms are equal in the expansion find all possible real values of .

• A
• B
• C
• D

Q18:

Determine if is the middle term in the binomial expansion of .

Q19:

What is the value of that makes the middle term of the binomial expansion of the following independent of ?

Q20:

Consider the expansion of in ascending powers of where . If the middle term in the expansion is five times the fifth term, what is the value of ?

• A
• B
• C
• D