There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer.
There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(76)-A(75)?
Answer/Solution
2^75
Steps/Work
A1= 3
A2= 2*3-1= 5
A3= 2*5-1= 9
A4= 2*9-1= 17
We can notice that there is a squence
A2-A1= 2^1
A3-A2= 2^2
A4-A3= 2^3
Hence A76-A75= 2^75
E is the answer
A2= 2*3-1= 5
A3= 2*5-1= 9
A4= 2*9-1= 17
We can notice that there is a squence
A2-A1= 2^1
A3-A2= 2^2
A4-A3= 2^3
Hence A76-A75= 2^75
E is the answer