An arithmetic series has first term $a$ and common difference $d$, where $a$ and $d$ are non-zero. T

Question

An arithmetic series has first term $a$ and common difference $d$, where $a$ and $d$ are non-zero. The first three terms of a geometric series are equal to the ninth, fifth and second terms respectively of the arithmetic series. Prove that the geometric series is convergent and find, in terms of $a$, the sum to infinity. [5] Given that $a>0$, find the largest value of $n$ for which the sum of the first $n$ terms of the geometric series is less than four fifths of the sum to infinity. [3]

Accepted Answer

$a = 8d$, $r = \frac{3}{4}$, $S_\infty = 8a$; largest $n = 5$

2011 IJC P1 Q7

2011 IJC P1 Q7

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