(a)[3]
Show that the relation $a^2 - 10ac + 9c^2 = 0$ holds.
(b(i))[5]
Determine the sum to infinity of the geometric progression.
(b(ii))[3]
Determine the sum of the first 20 terms of the arithmetic progression.
Mathematics 9709 · AS & A Level · Series
Series — practice question
The first three terms in a geometric progression are $a$, $b$ and $c$ respectively, with $a$, $b$ and $c$ all positive constants. The first three terms in an arithmetic progression are $a$, $b$ and $-3c$ respectively. You are told that $a = 9$ and that $c$ is the smaller of the two possible values.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the AP/GP condition: $-3c-b=b-a$ (or an equivalent form)” …
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