SOLUTION: The numbers a, b, c, d, and e are the first five terms in a sequence. Each term beginning with c is the sum of the previous two terms. If a= e= 9, find the value of 9

Question 641709: The numbers a, b, c, d, and e are the first five terms in a sequence. Each term beginning with c is the sum of the previous two terms. If a= e= 9, find the value of 9
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
A given sequence of numbers is a, b, c, d, e;
where, starting with c, that entry is the sum of the two previous entries.
This property gives us the following equations;
(1) c = a + b
(2) d = c + b = a + b + b = a + 2b
(3) e = d + c = a + 2b +a + b = 2a + 3b
Using the given values of a and e (each = 9) yields
(4) c = 9 + b
(5) d = 9 + 2b
(6) 9 = 18 + 3b
Solve (6) for b yields
(7) b = -3
Substitute b into (4) and (5) yields
(8) c = 9 + (-3) = 6
(9) d = 9 + 2(-3) = 9 - 6 = 3
The sequence is 9, -3, 6, 3, 9

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