SOLUTION: If the difference between the 3rd and the 1st term of a G.P is 42, and the 4th term is greater than the 2nd term by 168, what is the (1) common ratio, (2) 1st term. (3) 4th term of

Algebra ->  Sequences-and-series -> SOLUTION: If the difference between the 3rd and the 1st term of a G.P is 42, and the 4th term is greater than the 2nd term by 168, what is the (1) common ratio, (2) 1st term. (3) 4th term of      Log On


   

Question 769801: If the difference between the 3rd and the 1st term of a G.P is 42, and the 4th term is greater than the 2nd term by 168, what is the (1) common ratio, (2) 1st term. (3) 4th term of the progression
Found 2 solutions by reviewermath, oscargut:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
If the difference between the 3rd and the 1st term of a G.P is 42, and the 4th term is greater than the 2nd term by 168, what is the (1) common ratio, (2) 1st term. (3) 4th term of the progression
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A:
a%5B3%5D+-+a%5B1%5D = 42 ----> a%5B1%5Dr%5E2+-+a%5B1%5D = 42 -----> a%5B1%5D = 42%2F%28r%5E2-1%29
a%5B4%5D-a%5B2%5D = 168 ----> a%5B1%5Dr%5E3-a%5B1%5Dr = 168 ----> a%5B1%5D = 168%2F%28r%5E3-r%29
42%2F%28r%5E2-1%29 = 168%2F%28r%5E3-r%29
42r%5E3+-+42r = 168r%5E2+-+168
42r%5E3+-+168r%5E2+-+42r+%2B+168 = 0, divide by 42
r%5E3+-+4r%5E2+-+r+%2B+4 = 0
(r - 1)(r + 1)(r - 4) = 0
r = 1, -1, or 4
Disregard r = 1 and -1 because it will make a%5B1%5D undefined.
common ratio, r =highlight%284%29
1st term, a%5B1%5D = 42%2F%284%5E2-1%29 = highlight%2814%2F5%29
4th term, a%5B4%5D = a%5B1%5Dr%5E3 = %2814%2F5%29%2A%284%5E3%29 = highlight%28896%2F5%29

Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!

Answers:
1)4
2) 2.8
3) 179.2
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