| Exam Board | Edexcel |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2020 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Prove sum formula |
| Difficulty | Moderate -0.8 Part (i) is a standard bookwork proof of the arithmetic series formula that appears in every A-level textbook, requiring only pairing terms or writing the sum forwards and backwards. Part (ii) involves straightforward substitution and recognizing that the alternating terms cancel in pairs, making this a routine exercise testing basic understanding rather than problem-solving ability. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
8. (i) An arithmetic series has first term $a$ and common difference $d$.
Prove that the sum to $n$ terms of this series is
$$\frac { n } { 2 } \{ 2 a + ( n - 1 ) d \}$$
(ii) A sequence $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is given by
$$u _ { n } = 5 n + 3 ( - 1 ) ^ { n }$$
Find the value of
\begin{enumerate}[label=(\alph*)]
\item $u _ { 5 }$
\item $\sum _ { n = 1 } ^ { 59 } u _ { n }$\\
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel P2 2020 Q8 [7]}}