SPS SPS SM 2025 November — Question 5

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2025
SessionNovember
TopicArithmetic Sequences and Series
TypeFind term or common difference
DifficultyModerate -0.8 This is a straightforward arithmetic series question requiring only standard formula application. Part (a) uses S_n = n/2(2a + (n-1)d) with simple algebra, and part (b) solves two simultaneous linear equations. No problem-solving insight needed, just routine manipulation of well-known formulas—easier than average A-level questions.
Spec1.04h Arithmetic sequences: nth term and sum formulae

An arithmetic series has first term \(a\) and common difference \(d\). The sum of the first 29 terms is 1102.
  1. Show that \(a + 14d = 38\). (3 marks)
  2. The sum of the second term and the seventh term is 13. Find the value of \(a\) and the value of \(d\). (4 marks)

An arithmetic series has first term $a$ and common difference $d$.

The sum of the first 29 terms is 1102.

\begin{enumerate}[label=(\alph*)]
\item Show that $a + 14d = 38$. (3 marks)

\item The sum of the second term and the seventh term is 13.

Find the value of $a$ and the value of $d$. (4 marks)
\end{enumerate}

\hfill \mbox{\textit{SPS SPS SM 2025 Q5}}