SPS SPS SM 2023 October — Question 5

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2023
SessionOctober
TopicArithmetic Sequences and Series

5. A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by $$u _ { 1 } = 8 \quad \text { and } \quad u _ { n + 1 } = u _ { n } + 3 .$$
  1. Show that \(u _ { 5 } = 20\).
  2. The \(n\)th term of the sequence can be written in the form \(u _ { n } = p n + q\). State the values of \(p\) and \(q\).
  3. State what type of sequence it is.
  4. Find the value of \(N\) such that \(\sum _ { n = 1 } ^ { 2 N } u _ { n } - \sum _ { n = 1 } ^ { N } u _ { n } = 1256\).
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