# Worksheet: Ratio between Two Consecutive Terms in a Binomial

Q1:

Consider the expansion of . Find the ratio between the eighth and the seventh terms.

• A
• B
• C
• D
• E

Q2:

Find the value of given that the ratio between and , in the expansion of , equals the ratio between and in the expansion of .

Q3:

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

• A
• B
• C
• D

Q4:

Determine the ratio of the coefficient of in to the coefficient of in . Note that for , we have .

• A
• B
• C
• D

Q5:

Consider the expansion of . Find the value of given that and the ratio between and is equal to .

Q6:

The coefficients of three consecutive terms in the expansion of are 230, 690, and 1β380 respectively. Evaluate and find their orders.

• A11, , ,
• B11, , ,
• C11, , ,
• D11, , ,

Q7:

Consider the expansion of . Find given that the ratio between and is .

• A
• B
• C
• D

Q8:

Consider the expansion of in ascending powers of . Given that the ratio between the coefficient of the fourth term and the coefficient of the second term is , determine the value of .

Q9:

Consider the expansion of . 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:

The ratio between the coefficients of three consecutive terms in the expansion of is . Evaluate and find the orders of these terms.

• A22, , ,
• B44, , ,
• C22, , ,
• D44, , ,

Q11:

Consider the expansion of If the ratio between the middle term and the term containing is , determine the value of .

• A4
• B
• C
• D2

Q12:

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 ,

Q13:

Note that . Given that the ratio between the coefficient of in the binomial expansion of and the coefficient of in the expansion of is , find the value of .

Q14:

Find given that the ratio between the sixth and the seventh terms in the expansion of is equal to .

• A
• B
• C
• D

Q15:

Find given that the ratio between the second and the third terms in the expansion of is equal to .

• A
• B
• C
• D

Q16:

Find given that the ratio between the ninth and the tenth terms in the expansion of is equal to .

• A
• B
• C
• D

Q17:

Consider the expansion of in ascending powers of . Given that the ratio between the thirteenth term and the twelfth term is , find the value of .

• A
• B
• C2
• D