Moderate -0.8 This is a straightforward application of standard arithmetic progression formulas. Part (a) requires solving two simultaneous equations (a+2d=24, a+9d=3) using routine algebraic manipulation. Part (b) requires calculating Sā ā-Sāā using the sum formula, which is a direct application once a and d are known. No problem-solving insight needed, just methodical application of memorized formulas.
6 The third term of an arithmetic progression is 24 . The tenth term is 3 .
Find the first term and the common difference.
Find also the sum of the 21st to 50th terms inclusive.
ft their \(a\) and \(d\); M1 for \(S_{30} = \frac{30}{2}(u_{21}+u_{50})\) o.e.
\(-2205\) cao
A1
B2 for \(-2205\) www
**Question 6:**
| Answer | Mark | Guidance |
|--------|------|----------|
| $a+2d=24$ and $a+9d=3$ | **M1** | | |
| $d=-3;\ a=30$ | **A1** | if **M0**, **B2** for either, **B3** for both | do not award **B2** or **B3** if values clearly obtained fortuitously |
| $S_{50} - S_{20}$ | **M1** | ft their $a$ and $d$; **M1** for $S_{30} = \frac{30}{2}(u_{21}+u_{50})$ o.e. | $S_{50}=-2175;\ S_{20}=30$; $u_{21}=30-20\times3=-30$; $u_{50}=30-49\times3=-117$ |
| $-2205$ cao | **A1** | **B2** for $-2205$ www | |
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6 The third term of an arithmetic progression is 24 . The tenth term is 3 .\\
Find the first term and the common difference.
Find also the sum of the 21st to 50th terms inclusive.
\hfill \mbox{\textit{OCR MEI C2 2011 Q6 [5]}}