$1$, $a$ and $b$ are three consecutive terms of a convergent geometric progression. It is give

Question

$1$, $a$ and $b$ are three consecutive terms of a convergent geometric progression. It is given that $a$, $b$ and $2$ are also three consecutive terms of an arithmetic progression. Find the value of $a$.[4] A particular airline company has been raising its ticket prices at a constant rate of $3\%$ per year since $1961$. If an air ticket from Country $X$ to Country $Y$ cost $\$150$ in $1961$, calculate to the nearest dollar, how much it will cost in $2009$. [3] Starting from the year $1990$, Mr. Wong has been buying a ticket from Country $X$ to Country $Y$ for himself every year. Calculate how much he had spent on the tickets, to the nearest dollar, from $1991$ to $2009$ inclusive. [3]

Accepted Answer

(a) $a = -0.781$ ( $3$ s.f.) (b)(i) Thus, it costs $\$ 620$ (to the nearest dollar) in $2009$. (ii) Thus, he had spent $\$9145$ (to the nearest dollar) from $1991$ to $2009$ inclusive.

2009 PJC CT Q10

2009 PJC CT Q10

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