OCR C4 — Question 3

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
TopicGeneralised Binomial Theorem
TypeFinding unknown power and constant

3. The first four terms in the series expansion of \(( 1 + a x ) ^ { n }\) in ascending powers of \(x\) are $$1 - 4 x + 24 x ^ { 2 } + k x ^ { 3 }$$ where \(a , n\) and \(k\) are constants and \(| a x | < 1\).
  1. Find the values of \(a\) and \(n\).
  2. Show that \(k = - 160\).