Edexcel C1 2012 June — Question 6 10 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2012
SessionJune
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicArithmetic Sequences and Series
TypeReal-world AP: find n satisfying a condition
DifficultyModerate -0.8 This is a straightforward application of standard arithmetic sequence formulas (nth term and sum) with minimal problem-solving required. Part (c) involves simple algebraic manipulation to reach a given result, and part (d) is trivial pattern recognition. The context is accessible and all steps follow directly from memorized formulas.
Spec1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum

6. A boy saves some money over a period of 60 weeks. He saves 10 p in week 1 , 15 p in week \(2,20 \mathrm { p }\) in week 3 and so on until week 60 . His weekly savings form an arithmetic sequence.
  1. Find how much he saves in week 15
  2. Calculate the total amount he saves over the 60 week period. The boy's sister also saves some money each week over a period of \(m\) weeks. She saves 10 p in week \(1,20 \mathrm { p }\) in week \(2,30 \mathrm { p }\) in week 3 and so on so that her weekly savings form an arithmetic sequence. She saves a total of \(\pounds 63\) in the \(m\) weeks.
  3. Show that $$m ( m + 1 ) = 35 \times 36$$
  4. Hence write down the value of \(m\).

6. A boy saves some money over a period of 60 weeks. He saves 10 p in week 1 , 15 p in week $2,20 \mathrm { p }$ in week 3 and so on until week 60 . His weekly savings form an arithmetic sequence.
\begin{enumerate}[label=(\alph*)]
\item Find how much he saves in week 15
\item Calculate the total amount he saves over the 60 week period.

The boy's sister also saves some money each week over a period of $m$ weeks. She saves 10 p in week $1,20 \mathrm { p }$ in week $2,30 \mathrm { p }$ in week 3 and so on so that her weekly savings form an arithmetic sequence. She saves a total of $\pounds 63$ in the $m$ weeks.
\item Show that

$$m ( m + 1 ) = 35 \times 36$$
\item Hence write down the value of $m$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel C1 2012 Q6 [10]}}