Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Ratio between Two Consecutive Terms in a Binomial

Q1:

Consider the expansion of ( 8 π‘₯ + 2 𝑦 ) 2 3 . Find the ratio between the eighth and the seventh terms.

  • A 1 7 π‘₯ 2 8 𝑦
  • B 2 8 𝑦 1 7 π‘₯
  • C 2 8 π‘₯ 1 7 𝑦
  • D 1 7 𝑦 2 8 π‘₯
  • E 8 π‘₯ 𝑦

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 ( π‘₯ βˆ’ 1 2 ) 1 9 .

  • A 1 2 π‘₯ 2
  • B π‘₯ 1 2
  • C 1 2 π‘₯
  • D π‘₯ 1 2 2

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 1 380 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 ο€Ό 5 2 + 2 π‘₯ 5  𝑛 in ascending powers of π‘₯ . Given that the ratio between the coefficient of the fourth term and the coefficient of the second term is 1 7 6 ∢ 3 7 5 , determine the value of 𝑛 .

Q9:

Consider the expansion of ( π‘š π‘₯ + 8 ) 𝑛 . Determine the values of π‘š and 𝑛 , given that the ratio between the coefficients of π‘Ž 1 2 and π‘Ž 1 4 is equal to 6 3 7 4 6 4 0 and that the ratio between the coefficients of π‘Ž 7 and π‘Ž 9 is equal to 4 9 1 3 6 0 .

  • A 𝑛 = 3 4 , π‘š = 7
  • B 𝑛 = 7 , π‘š = 4 1
  • C 𝑛 = 7 , π‘š = 3 4
  • D 𝑛 = 4 1 , π‘š = 7

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 π‘₯ βˆ’ 1 1 is 2 0 ∢ 2 1 , determine the value of π‘₯ .

  • A4
  • B 1 2
  • C 1 4
  • 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 π‘₯ given that the ratio between the sixth and the seventh terms in the expansion of ο€Ό 1 2 π‘₯ + 6 π‘₯  2 1 0 is equal to 7 5 ∢ 2 .

  • A 1 2 5 8
  • B 2 5
  • C 8 1 2 5
  • D 5 2

Q15:

Find π‘₯ given that the ratio between the second and the third terms in the expansion of ο€Ό 1 5 π‘₯ + 2 π‘₯  2 1 1 is equal to 1 2 5 ∢ 1 8 .

  • A 1 2 5 2 7
  • B 3 5
  • C 2 7 1 2 5
  • D 5 3

Q16:

Find π‘₯ given that the ratio between the ninth and the tenth terms in the expansion of ο€Ό 1 5 π‘₯ + 8 π‘₯  2 1 2 is equal to 8 ∢ 9 .

  • A 8 2 7
  • B 3 2
  • C 2 7 8
  • D 2 3

Q17:

Consider the expansion of ( 3 + 6 π‘₯ ) 1 3 in ascending powers of π‘₯ . Given that the ratio between the thirteenth term and the twelfth term is 3 ∢ 2 , find the value of π‘₯ .

  • A 1 2
  • B 2 9
  • C2
  • D 9 2