Question

the number 1 is written on a piece of paper and then passed around the room to each of the 50 students in turn. each of the students must cross out the numbers seen and replace it with I s double plus one. what is the final result​

Answer 1

The last term on the paper after 50 students =
`2^((50)) -1`

Explanation:

The general term of the equation:

Here, the first term = 1

Second term = 2(1) + 1 = 3 = 4 - 1 =
`2^(2)  - 1`

Third Term = 2(a2) + 1 = 2(3) + 1 = 7 = 8 -1 =
`2^(3)  - 1`

Fourth term = 2( a3) + 1 = 2(7) + 1 = 15 = 16 - 1 =
`2^(3)  - 1`

Continuing this way, we get

Last term :
`a_n = 2^n  -1`

So, the 50th term of this sequence is

`a_((50)) = 2^((50)) -1`

Hence, the last term on the paper after 50th student changes it =
`2^((50)) -1`