SOLUTION: 2x-4;x+5 and 3x-1 are the first three terms of an arithmetic sequence.(I) show that x=5 and write the first three terms of the sequence
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Question 1070563: 2x-4;x+5 and 3x-1 are the first three terms of an arithmetic sequence.(I) show that x=5 and write the first three terms of the sequence Answer by ikleyn(52803) (Show Source):
You are given
= 2x-4; = x+5; = 3x-1.
Since they are three consecutive terms of an arithmetic progression,
= (each side is the common difference of the progression).
It gives you an equation
(x+5) - (2x-4) = (3x-1) - (x+5).
Simplify and solve for x:
-x + 9 = 2x - 6,
9 + 6 = 2x + x ---> 15 = 3x ---> x = = 5.
The three terms of the sequence are
= 2*5-4 = 6;
= 5 + 5 = 10;
= 3*5-1 = 14.
