Question

The number 1 is written on a piece of paper and passed around the room to each 50 students.each student cross out the number they seen and double it and add one. the he final student does this and then announces the final number .what is it?​

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