OCR C2 — Question 1

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
TopicArithmetic Sequences and Series
  1. The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$u _ { n } = 2 ^ { n } + k n ,$$ where \(k\) is a constant.
Given that \(u _ { 1 } = u _ { 3 }\),
  1. find the value of \(k\),
  2. find the value of \(u _ { 5 }\).
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