SOLUTION: what is the first five terms and 50th term of this sequence. An=2a n-1 + 5 and a1=3

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Question 1168283: what is the first five terms and 50th term of this sequence.
An=2a n-1 + 5 and a1=3
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Follow the instructions to find the first 5 terms recursively:

a(1) = 3
a(2) = 2*a(1)+5 = 6+5 = 11
a(3) = 2*a(2)+5 = 22+5 = 27
a(4) = 2*a(3)+5 = 54+5 = 59
a(5) = 2*a(4)+5 = 118+5 = 123

Look for the pattern to deduce the formula for the n-th term.

The numbers are approximately doubling each time; so compare the sequence to appropriate powers of 2:
  this sequence:   3   11   27   59  123
  powers of 2:     8   16   32   64  128
                   ---------------------
  differences:     5    5    5    5    5


The n-th term in the sequence is 5 less than 2 to the power (n+2):

t%28n%29+=+2%5E%28n%2B2%29-5

So the 50th term is 2%5E52%2B5, which is a huge number....