Find n and constants from given terms

The first few terms of the expansion are given explicitly as an expression (e.g., 32 - 40x + bx^2) and the question asks to find n and other unknown constants a, b, etc.

5 questions · Moderate -0.2

Sort by: Default | Easiest first | Hardest first
CAIE P1 2006 June Q4
5 marks Moderate -0.8
4 The first three terms in the expansion of \(( 2 + a x ) ^ { n }\), in ascending powers of \(x\), are \(32 - 40 x + b x ^ { 2 }\). Find the values of the constants \(n , a\) and \(b\).
Edexcel C2 Q2
7 marks Moderate -0.3
The expansion of \((2 - px)^6\) in ascending powers of \(x\), as far as the term in \(x^2\), is $$64 + Ax + 135x^2.$$ Given that \(p > 0\), find the value of \(p\) and the value of \(A\). [7]
Edexcel C2 Q4
7 marks Standard +0.8
The first three terms in the expansion, in ascending powers of x, of (1 + px)ⁿ, are 1 - 18x + 36p²x². Given that n is a positive integer, find the value of n and the value of p. [7]
Edexcel C2 Q5
7 marks Moderate -0.3
The expansion of \((2 - px)^6\) in ascending powers of \(x\), as far as the term in \(x^2\), is $$64 + Ax + 135x^2.$$ Given that \(p > 0\), find the value of \(p\) and the value of \(A\). [7]
Edexcel AS Paper 1 Q11
6 marks Moderate -0.3
The first 3 terms, in ascending powers of \(x\), in the binomial expansion of \((1 + kx)^{10}\) are given by $$1 + 15x + px^2$$ where \(k\) and \(p\) are constants.
  1. Find the value of \(k\) [2]
  2. Find the value of \(p\) [2]
  3. Given that, in the expansion of \((1 + kx)^{10}\), the coefficient of \(x^4\) is \(q\), find the value of \(q\). [2]