# Lesson Worksheet: General Term in the Binomial Theorem Mathematics

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 the third term in the expansion of .

• A
• B
• C
• D

Q2:

Find in the expansion of .

• A
• B
• C
• D
• E

Q3:

Determine the coefficient of in the expansion of .

Q4:

The terms of the expansion of are arranged according to the descending powers of . Given that , find the value of .

Q5:

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

• A
• B
• C
• D

Q6:

Consider the expansion of . Find the ratio between the eighth and the seventh terms, when written in descending powers of .

• A
• B
• C
• D
• E

Q7:

Consider the expansion of , where is positive. Find the values of , , and given that , , and .

• A, ,
• B, ,
• C, ,
• D, ,

Q8:

Consider the binomial expansion of in ascending powers of . When , one of the terms in the expansion is equal to twice its following term. Find the position of these two terms.

• A,
• B,
• C,
• D,

Q9:

Consider the expansion of , where is a positive constant. Determine the values of and , given that the ratio between the coefficients of and is equal to and that the ratio between the coefficients of and is equal to .

• A,
• B,
• C,
• D,

Q10:

Find the ratio between the fifteenth and seventeenth terms in the expansion of .

• A
• B
• C
• D