The value of a rare comic book is expected to follow a geometric sequence from year to year. It is presently worth $800 and is expected to be worth $1250 two years from now. How much is the comic book expected to be worth one year from now and three years from now?

you add 1/4 each year: 800 to 1000 in one year 1000 to 1250 in 2 1250 to around 1812.5

Answered by MicahSE | 2024-06-10

The value of the rare comic book, which is following a geometric sequence, can be determined using the formula for the nth term of a geometric sequence: Vn = V1 × r(n-1) , where Vn is the value of the nth year, V1 is the initial value, r is the common ratio, and n is the number of years.
We are given that V1 = $800 and V3 = $1250. To find the common ratio, we use the two years between the given values, so:
1250 = 800 × r(3-1) , which simplifies to 1250 = 800 × r2
The common ratio r can then be found by dividing 1250 by 800 and taking the square root, so r ≈ 1.25 . To find the expected value after one year (V2), we compute 800 × 1.25(2-1) , which equals $1000.
Similarly, to find the expected value after three years (V4), we compute 800 × 1.25(4-1) , which equals $1562.50.

Answered by qwcat | 2024-06-24

The comic book is expected to be worth $1000 one year from now and approximately $1562.50 three years from now, using the common ratio derived from its initial and future values.
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Answered by qwcat | 2024-12-20