tmua.me Extreme Set A Paper 2 · Question 14

A geometric progression has terms

a_n=a r^{n-1}\qquad(n=1,2,3,\ldots),

where $a>0$ and $r>0$ . It is known that $a_2$ , $a_5$ and $a_9$ are integers.

Consider the condition $r\geq1$ and the statement that infinitely many terms of the progression are integers.

Which of the following correctly describes the condition in relation to the statement?

AThe condition is necessary but not sufficient.

BThe condition is sufficient but not necessary.

CThe condition is both necessary and sufficient.

DThe condition is neither necessary nor sufficient.

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