Question

The selling price of a certain collector’s item was $10 in 2000 and $15 in 2001. If the selling price of the item follows a geometric sequence, what would the price of the item be in 2002?

Answer 1

$20

Explanation:

the pattern is very simple

2000= $10

2001= $15

2002= $20

2003= $25

And so on

Answer 2

The price of the item in 2002 would be $22.5

Explanation:

Recall that the nth term of a geometric sequence of first term
`a_1` (in our case $10), is given by the formula:

`a_n=a_1\,\,r^(n-1)`

where "r" is the common ratio obtained by the quotient of a term of the sequence divided by the previous term. In this case such common ratio is given by the quotient of $15 divided the previous value $10,

That is:

`r=(15)/(10) =(3)/(2)= 1.5`

Then the price of the item in the year 2002 (which is the third term of the sequence; n = 3) is given by:

`a_3=a_1\,\,r^(3-1)\\a_3=10\,\,r^(2)\\a_3=10\,\,((3)/(2)) ^(2)\\a_3=(45)/(2) \\a_3=22.5`

That is, the price of the item would be $22.5