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Question 1143022: Please someone throughly explain this question and solve it step by step so that I can understand, thank you and god bless you. :D
The terms 4x + 36, 2x + 15, and 3x - 30 are consecutive terms in an arithmetic sequence. The value of x is
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have an arithmetic sequence.
the formula for an arithmetic sequence is An = A1 + (n-1) * d
An is the nth term.
A1 is the first term.
n is the term number
d is the common difference between each term in the sequence.
the key here is that the difference between each term in the sequence has to be the same.
therefore, the difference between the second term and the first term has to be the same as the difference between the third term and the second term.
what this tells you is that (2x + 15) - (4x + 36) = (3x - 30) - (2x + 15).
simplify to get:
2x + 15 - 4x - 36 = 3x - 30 - 2x - 15
combiine like terms to get:
-2x - 21 = x - 45
subtract x from both sides of the equation and add 45 to both sides of the equation to get:
-3x + 24 = 0
add 3x to both sides of the equation and solve for x to get x = 24 / 3 = 8.
if done correctly, the value of x has to be equal to 8.
using 8 as the value of x, you get:
4x + 36 = 68
2x + 15 = 31
3x - 30 = -6
31 - 68 = -37
-6 - 31 = -37
the common difference is -37.
the value of 8 for x gives you an arithmetic sequence where the common difference is -37.
x = 8 is your solution.
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