SOLUTION: The first term of a geometric sequence is 2, and the 4th term is 250. Find the 2 terms between the first and the 4th term.

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Question 1207190: The first term of a geometric sequence is 2, and the 4th term is 250. Find the 2 terms between the first and the 4th term.
Answer by ikleyn(52767) About Me  (Show Source):
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The first term of a geometric sequence is 2, and the 4th term is 250.
Find the 2 terms between the first and the 4th term.
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    a%5B1%5D = 2,

    a%5B4%5D = a%5B1%5D%2Ar%5E3 = 250.


Hence,  

    2%2Ar%5E3 = 250

     r%5E3 = 250/2 = 125

      r = root%283%2C125%29 = 5.


The two terms between the first and the 4th terms are

    a%5B2%5D = r%2Aa%5B1%5D = 5*2 = 10,

     a%5B3%5D = r%2Aa%5B2%5D = 5*10 = 50.

Solved.

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On geometric progressions,  see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.