SOLUTION: Write out the first four terms of the following sequences. b1 = 8, bk + 1 = 2bk + 1, k ≥ 1

Algebra ->  Sequences-and-series -> SOLUTION: Write out the first four terms of the following sequences. b1 = 8, bk + 1 = 2bk + 1, k ≥ 1      Log On


   

Question 968052: Write out the first four terms of the following sequences.
b1 = 8, bk + 1 = 2bk + 1, k ≥ 1
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
b%5B1%5D+=+8, b%5Bk+%2B+1%5D+=+2b%5Bk%5D+%2B+1, k+%3E=+1

The first term is given as b%5B1%5D=8

To find b2, plug in k=1 and b%5B1%5D=8 and simplify:

b%5Bk%2B1%5D+=+2b%5Bk%5D+%2B+1
b%5B1+%2B+1%5D+=+2b%5B1%5D+%2B+1
b%5B2%5D+=+2%288%29+%2B+1
b%5B2%5D+=+16+%2B+1
b%5B2%5D+=+17

To find b3, plug in k=2 and b%5B2%5D=17 and simplify:

b%5Bk+%2B+1%5D+=+2b%5Bk%5D+%2B+1
b%5B2+%2B+1%5D+=+2b%5B2%5D+%2B+1
b%5B3%5D+=+2%2817%29+%2B+1
b%5B3%5D+=+34+%2B+1
b%5B3%5D+=+35

To find b4, plug in k=3 and b%5B3%5D=35 and simplify:

You finish.

Edwin