Question

a gas-filled balloon rises 40 feet in the 1st minute, 60 feet in the 2nd minute, and 80 feet in the 3rd minute, how many feet will the balloon rise during the 15th minute?

Answer 1

Let
`g_n` represent the number of feet that the balloon rises in the
`n^(th)` minute.

so


`g_1=40` ft , means that in the 1st minute, the balloon rose 40 feet


`g_2=60` ft, means : in the 2nd minute the balloon rose 60 feet


`g_3=80`

we notice that each minute, the balloon rises a multiple of 20, feet:


`g_1=40=2*20`


`g_2=60=3*20`


`g_3=80=4*20`

so it is clear that
`g_n=(n+1)*20`

during the 15th minute the balloon rises
`g_1_5=16*20=320`(feet)


Answer: 320