The sequence can be expressed by the formula: v(n) = 5000 . (3/4)ⁿ⁻¹. Helium left at the start of the 10th day is 375.42 cm³
1st day:
Helium is filled with 5000 cm³ of helium.
We can write v(1) = 5000 cm³
2nd day:
The balloon losses 1/4 of helium volume. In other word, the remaining volume of helium is:
(1 - 1/4) = 3/4 of its initial volume.
We can write:
v(2) = 3/4 . 5000 = 3750 cm³
We can continue this process:
v(3) = 3/4 . 3750 = 2812.5
Notice that each day remaining volume of helium forms a geometric sequence, with v(1) = 5000 and a common ratio (r) = 3/4.
Recall the formula for the nth term of a geometric sequence:
v(n) = v(1) . rⁿ⁻¹
To find the explicit formula, substitute v(1) = 5000 and (r) = 3/4:
v(n) = 5000 . (3/4)ⁿ⁻¹
Tenth day means n = 10. Substitute these parameters into the formula:
v(10) = 5000 . (3/4)¹⁰⁻¹
v(10) = 5000 . (3/4)⁹
= 375.42 cm³
Learn more about geometric sequence here:
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