Moderate -0.3 This is a straightforward application of standard arithmetic progression formulas (nth term and sum formulas) requiring two simultaneous equations to find a and d, then calculating Sā ā. While it involves multiple steps and algebraic manipulation, it follows a routine procedure with no conceptual challenges or novel problem-solving required, making it slightly easier than average.
2 The thirteenth term of an arithmetic progression is 12 and the sum of the first 30 terms is - 15 .
Find the sum of the first 50 terms of the progression.
For correct equation in \(a\) and \(d\). If using \(\dfrac{n}{2}(a+l)\), must replace \(l\) with an expression involving \(a\) and \(d\)
\(a = 72,\ d = -5\)
B1
Both values correct SOI
\(S_{50} = \dfrac{50}{2}(2(\text{their } a) + 49(\text{their } d))\)
M1
Using sum formula with *their* \(a\) and \(d\) values obtained via a valid method
\(S_{50} = -2525\)
A1
5
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $a + 12d = 12$ | B1 | For correct equation |
| $\dfrac{30}{2}(2a + (30-1)d) = -15$ | B1 | For correct equation in $a$ and $d$. If using $\dfrac{n}{2}(a+l)$, must replace $l$ with an expression involving $a$ and $d$ |
| $a = 72,\ d = -5$ | B1 | Both values correct SOI |
| $S_{50} = \dfrac{50}{2}(2(\text{their } a) + 49(\text{their } d))$ | M1 | Using sum formula with *their* $a$ and $d$ values obtained via a valid method |
| $S_{50} = -2525$ | A1 | |
| | **5** | |
2 The thirteenth term of an arithmetic progression is 12 and the sum of the first 30 terms is - 15 .\\
Find the sum of the first 50 terms of the progression.\\
\hfill \mbox{\textit{CAIE P1 2022 Q2 [5]}}