Easy -1.2 This is a straightforward arithmetic sequence problem requiring only substitution into the nth term formula and solving a simple linear equation. It's below average difficulty as it tests basic recall and algebraic manipulation with no problem-solving insight needed.
\((n-1)d = 77\), \((3n-1)d = 238\) SOI OR \(2nd = 161\) explicitly stated
1 B1
\(\frac{n-1}{3n-1} = \frac{77}{238}\)
1 M1
must be from correct \(u_n\) formula OR other attempt to eliminate \(d\); substitute \(d = \frac{161}{2n}\); (If \(n\) is eliminated \(d\) must be found)
\(n = 23\) (\(d = \frac{77}{22} = 3.5\))
1 A1
Total
4
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $7 + (n-1)d = 84$ and/or $7 + (3n-1)d = 245$ | 1 B1 | |
| $(n-1)d = 77$, $(3n-1)d = 238$ SOI OR $2nd = 161$ explicitly stated | 1 B1 | |
| $\frac{n-1}{3n-1} = \frac{77}{238}$ | 1 M1 | must be from correct $u_n$ formula OR other attempt to eliminate $d$; substitute $d = \frac{161}{2n}$; (If $n$ is eliminated $d$ must be found) |
| $n = 23$ ($d = \frac{77}{22} = 3.5$) | 1 A1 | |
| **Total** | **4** | |
3 An arithmetic progression has first term 7. The $n$th term is 84 and the ( $3 n$ )th term is 245 .\\
Find the value of $n$.\\
\hfill \mbox{\textit{CAIE P1 2020 Q3 [4]}}