Standard +0.3 This is a straightforward problem requiring students to set up equations using AP and GP formulas, then solve for d. The algebra is simple (quadratic equation), and showing the sequence is increasing just requires checking d > 0. Slightly easier than average as it's a standard textbook-style question with clear structure and no conceptual surprises.
An arithmetic progression has first term \(2\) and common difference \(d\), where \(d \neq 0\). The first, third and thirteenth terms of this progression are also the first, second and third terms, respectively, of a geometric progression.
By determining \(d\), show that the arithmetic progression is an increasing sequence. [5]
An arithmetic progression has first term $2$ and common difference $d$, where $d \neq 0$. The first, third and thirteenth terms of this progression are also the first, second and third terms, respectively, of a geometric progression.
By determining $d$, show that the arithmetic progression is an increasing sequence. [5]
\hfill \mbox{\textit{OCR H240/03 2021 Q3 [5]}}