sferguson sferguson
  • 03-07-2017
  • Mathematics
contestada

Solve by unfolding: a0=2, and, n>=1, a_n=7a_n-1.

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altavistard
altavistard altavistard
  • 03-07-2017
We are told that the first term is 2.  The next term is 7(2) = 14; the third term is 7(14) = 98.  And so on.  So, the first term and the common ratio (7) are known.

The nth term of this geometric series is a_n = 2(7)^(n-1).

Check:  What is the first term?  We expect it is 2.  2(7)^(1-1) = 2(1) = 2.  Correct.

What is the third term?  We expect it is 98.  2(7)^(3-1) = 2(7)^2 = 98.  Right.
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