Moderate -0.5 This is a straightforward application of standard GP formulas with clear given information. Students substitute r = -0.5 and S₃ = 15 into the sum formula to find a, then use S∞ = a/(1-r). The negative ratio adds minor complexity but the problem requires only direct formula application with no problem-solving insight.
Use of G.P. sum formula or attempt to sum three terms
\(\frac{3a}{4} = 15 \Rightarrow a = 20\)
A1, A1
Forming an equation for \(a - \frac{a}{2} + \frac{a}{4} = 15\)
M1
Substitute numerical values into \(\frac{a}{1-r}\)
M1, A1
\(13\frac{1}{3}\)
Total: 5 marks
$\frac{a(1-(-0.5)^3)}{1-(-0.5)} = 15$ | M1 | Use of G.P. sum formula or attempt to sum three terms
$\frac{3a}{4} = 15 \Rightarrow a = 20$ | A1, A1 |
Forming an equation for $a - \frac{a}{2} + \frac{a}{4} = 15$ | M1 |
Substitute numerical values into $\frac{a}{1-r}$ | M1, A1 |
$13\frac{1}{3}$ | | **Total: 5 marks**
1 The common ratio of a geometric progression is - 0.5 . The sum of its first three terms is 15 . Find the first term.\\
Find also the sum to infinity.
\hfill \mbox{\textit{OCR MEI C2 Q1 [5]}}