The terms 5x + 2, 7x - 4, and 10x + 6 are consecutive terms of an arithmetic sequence. Determine the value of x and state the three terms.
Thank you very much!
Thank you very much!
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The difference between consecutive terms is equal in an arithmetic sequence. Gotta know that first. Now that you have been enlightened, do you know how to do it? If you do, great. If you don't continue below.
Since the difference between consecutive terms is equal, (10x + 6) - (7x - 4) is equal to (7x - 4) - (5x + 2).
Now do you know how to do it? If you still don't, no worries, you are not retarded. You just need to brush up your algebra skills. Continue reading.
(10x + 6) - (7x - 4) becomes 10x - 7x + 6 - (-4) becomes 3x + 10
(7x - 4) - (5x + 2) becomes 7x - 5x - 4 - 2 becomes 2x - 6
So you get 3x + 10 = 2x - 6
Isolate the terms by moving the like terms to the same side:
3x - 2x = -10 - 6
x = -16
Are we done? NO! Hell no!
The question asks for the three terms as well! Watch out for this. Many questions are like this. You find out your x value but that isn't what the question actually asks for.
Anyway, since x = -16, you simply insert that into your three values.
5(-16) + 2 = -78
7(-16) - 4 = -116
10(-16) + 6 = -154
The three terms are -78, -116, -154.
Just to make sure, check your work. Like I mentioned before, the difference between consecutive terms in a arithmetic sequence are equal. Which implies that if the three answers are correct, then -154 - (-116) and -116 - (-78) should be equal. Which is true. The common difference is -38.
You are done. Yay.
Hope this helped!
Since the difference between consecutive terms is equal, (10x + 6) - (7x - 4) is equal to (7x - 4) - (5x + 2).
Now do you know how to do it? If you still don't, no worries, you are not retarded. You just need to brush up your algebra skills. Continue reading.
(10x + 6) - (7x - 4) becomes 10x - 7x + 6 - (-4) becomes 3x + 10
(7x - 4) - (5x + 2) becomes 7x - 5x - 4 - 2 becomes 2x - 6
So you get 3x + 10 = 2x - 6
Isolate the terms by moving the like terms to the same side:
3x - 2x = -10 - 6
x = -16
Are we done? NO! Hell no!
The question asks for the three terms as well! Watch out for this. Many questions are like this. You find out your x value but that isn't what the question actually asks for.
Anyway, since x = -16, you simply insert that into your three values.
5(-16) + 2 = -78
7(-16) - 4 = -116
10(-16) + 6 = -154
The three terms are -78, -116, -154.
Just to make sure, check your work. Like I mentioned before, the difference between consecutive terms in a arithmetic sequence are equal. Which implies that if the three answers are correct, then -154 - (-116) and -116 - (-78) should be equal. Which is true. The common difference is -38.
You are done. Yay.
Hope this helped!
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since it is arithmetic ... (10x + 6) - (7x - 4) = (7x-4) - (5x+2) the difference between the terms
now collect and solve for x
3x + 10 = 2x - 6 ==> x = -16
terms are: -78 , -116 , -154
now collect and solve for x
3x + 10 = 2x - 6 ==> x = -16
terms are: -78 , -116 , -154