The sequence {an) is defined by ao = 1 and An+1=2an +1 for n = 0,1,2, What is the value
of a4?

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Work Shown:

Use the value of a0 to find the value of a1. The idea is you double the previous value, and then add 1.

Which is then used to find the value of a2. Follow the same process as before (double the previous value and then add 1).

This is used to find a3

Finally we can now find a4

Recursive sequences like this aren't too bad if n is small, but as n gets larger, things become more tedious. For those cases, its best to try to find a closed form equation. If not, then the next best thing is using a spreadsheet to automate the process.

1: -2 3/4, -2 1/2, -14, 0, 3, 8 1/3

2: -4, -3, -2 1/2, -2 1/4, 3 1/4,

step-by-step explanation:

the answer is 8/21

hope this