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# Worksheet: General Term in the Binomial Theorem

Q1:

Find the third term in the expansion of .

• A
• B
• C
• D

Q2:

Find the value of that satisfies

Q3:

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

Q4:

Find in the expansion of .

• A
• B
• C
• D
• E

Q5:

Find in the expansion of .

• A
• B
• C
• D
• E

Q6:

Find the third term in the expansion of .

• A
• B
• C
• D

Q7:

Find in the expansion of .

• A
• B
• C
• D
• E

Q8:

Find in the expansion of .

• A
• B
• C
• D
• E

Q9:

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

• A
• B
• C
• D

Q10:

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

Q11:

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

Q12:

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 ?

Q13:

Find the coefficient of in the expansion of .

Q14:

Find the coefficient of in the expansion of .

Q15:

Find the third term in the expansion of .

• A
• B
• C
• D

Q16:

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

• A
• B
• C
• D

Q17:

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

• A
• B
• C
• D

Q18:

Find in the expansion of .

• A
• B
• C
• D

Q19:

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

• A4, 12
• B2, 14
• C2,
• D2, 1

Q20:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q21:

Find in the expansion of .

• A
• B
• C
• D

Q22:

Find in the expansion of .

• A
• B
• C
• D

Q23:

Find the second-to-last term in .

• A
• B
• C
• D

Q24:

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 ,

Q25:

Find the general term in .

• A
• B
• C
• D
• E