Respuesta :
Answer:
$20
Step-by-step explanation:
the pattern is very simple
2000= $10
2001= $15
2002= $20
2003= $25
And so on
Answer:
The price of the item in 2002 would be $22.5
Step-by-step explanation:
Recall that the nth term of a geometric sequence of first term [tex]a_1[/tex] (in our case $10), is given by the formula:
[tex]a_n=a_1\,\,r^{n-1}[/tex]
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:
[tex]r=\frac{15}{10} =\frac{3}{2}= 1.5[/tex]
Then the price of the item in the year 2002 (which is the third term of the sequence; n = 3) is given by:
[tex]a_3=a_1\,\,r^{3-1}\\a_3=10\,\,r^{2}\\a_3=10\,\,(\frac{3}{2}) ^{2}\\a_3=\frac{45}{2} \\a_3=22.5[/tex]
That is, the price of the item would be $22.5