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jeka94
3 years ago
6

The sequence {an) is defined by ao = 1 and

Mathematics
1 answer:
otez555 [7]3 years ago
6 0
<h3>Answer: 31</h3>

=======================================

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.

a_{n+1} = 2*(a_n) + 1\\\\a_{0+1} = 2*(a_0) + 1\\\\a_{1} = 2*(1) + 1\\\\a_{1} = 3\\\\

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

a_{n+1} = 2*(a_n) + 1\\\\a_{1+1} = 2*(a_1) + 1\\\\a_{2} = 2*(3) + 1\\\\a_{2} = 7\\\\

This is used to find a3

a_{n+1} = 2*(a_n) + 1\\\\a_{2+1} = 2*(a_2) + 1\\\\a_{3} = 2*(7) + 1\\\\a_{3} = 15\\\\

Finally we can now find a4

a_{n+1} = 2*(a_n) + 1\\\\a_{3+1} = 2*(a_3) + 1\\\\a_{4} = 2*(15) + 1\\\\a_{4} = 31\\\\

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.

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