Sequences & Series
Linear Recurrence Relations
Grade 11
Question:
<p>Let <i>a</i><sub>12</sub> =</p>
<p>(A) 2<i>a</i><sub>11</sub> + <i>a</i><sub>10</sub></p>
<p>(B) <i>a</i><sub>11</sub> − <i>a</i><sub>10</sub></p>
<p>(C) <i>a</i><sub>11</sub> + <i>a</i><sub>10</sub></p>
<p>(D) <i>a</i><sub>11</sub> + 2<i>a</i><sub>10</sub></p>
Step-by-Step Solution
Key Concept: The recurrence relation <i>a</i><sub><i>n</i>+2</sub> = <i>a</i><sub><i>n</i>+1</sub> + <i>a</i><sub><i>n</i></sub> directly gives <i>a</i><sub>12</sub>.
<p><strong>Step 1:</strong> From the recurrence relation established in Question 17: <i>a</i><sub><i>n</i>+2</sub> = <i>a</i><sub><i>n</i>+1</sub> + <i>a</i><sub><i>n</i></sub>.</p><p><strong>Step 2:</strong> Applying this for <i>n</i> = 10: <i>a</i><sub>12</sub> = <i>a</i><sub>11</sub> + <i>a</i><sub>10</sub>.</p><p>∴ Answer is C.</p>
Correct Answer: C