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padilas [110]
2 years ago
7

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 stud

ents must cross out the numbers seen and replace it with I s double plus one. what is the final result​
Mathematics
1 answer:
Gnom [1K]2 years ago
4 0

Answer:

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

Step-by-step 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

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