Point 6 of 8 — Lesson 1: Counting Principle, Permutations (nPr) and Combinations (nCr)Question bank: 5 questions (5 with pictures)
06 1-3 (a) The ratio between two consecutive terms
Ratio of terms
For consecutive termsandof:
For thecoefficients (when the terms are written with a common variable), the factor is replaced by the ratio of the coefficients of the second and first terms of the binomial.
For: .
Proof of the ratio: .
✍️ Worked examples
Example 14:In the expansion offindand the ratio.
Solution:
Fortake: .
.
has: .
has: .
.
Example 15:In the expansion of, if, find.
Solution:
Divide the equation by: .
, so.
.
; multiply by: .
, so.
Henceor, i.e. or.
Example 16: The coefficients of three consecutive terms of in ascending powers are. Find and the orders of the terms.
Solution:
Let the terms be.
, soand(1).
, soand(2).
Multiply (2) by 2: ; subtract (1): .
From (2): , so.
The terms are, and indeed, , .
📝 Question bank for this point
5 questions linked to this point only, 5 of them with pictures.
