| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Convergence conditions |
| Difficulty | Easy -1.2 This is a straightforward classification question requiring only pattern recognition and recall of definitions (convergent, periodic, neither). Part (i) is a geometric sequence with r=1/2 (convergent), (ii) is arithmetic with d=4 (divergent), and (iii) repeats every 4 terms (periodic). No calculations or problem-solving required—just applying basic definitions to obvious patterns. |
| Spec | 1.04f Sequence types: increasing, decreasing, periodic |
| Answer | Marks | Guidance |
|---|---|---|
| converging + valid reason | 1 | e.g. converges to 0, \(r = \frac{1}{2}\), difference between terms decreasing, sum of terms converges to 6, G.P. with \( |
| Answer | Marks | Guidance |
|---|---|---|
| neither + valid reason | 1 | e.g. divergent oe, A.P., \(d=4\) oe, convergent and periodic ruled out with correct reasons |
| Answer | Marks | Guidance |
|---|---|---|
| periodic + valid reason | 1 | e.g. repeating cycle of terms |
## Question 10(i):
| converging + valid reason | 1 | e.g. converges to 0, $r = \frac{1}{2}$, difference between terms decreasing, sum of terms converges to 6, G.P. with $|r| < 1$ |
## Question 10(ii):
| neither + valid reason | 1 | e.g. divergent oe, A.P., $d=4$ oe, convergent and periodic ruled out with correct reasons |
## Question 10(iii):
| periodic + valid reason | 1 | e.g. repeating cycle of terms |10 For each of the following sequences, state with a reason whether it is convergent, periodic or neither. Each sequence continues in the pattern established by the given terms.\\
(i) $3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \ldots$\\
(ii) $3,7,11,15 , \ldots$\\
(iii) $3,5 , - 3 , - 5,3,5 , - 3 , - 5 , \ldots$
\hfill \mbox{\textit{OCR MEI C2 Q10 [3]}}