SOLUTION: Hello again online tutors! Here's my question: If x-5, 2x, and 4x+6 are the first three terms of an arithmetic sequence, find x and the value of the three terms. Thank you to any

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Question 1111187: Hello again online tutors! Here's my question:
If x-5, 2x, and 4x+6 are the first three terms of an arithmetic sequence, find x and the value of the three terms.
Thank you to anyone who can help!
Amelia B
Found 2 solutions by ikleyn, phillywily:
Answer by ikleyn(52787) (Show Source):
You can put this solution on YOUR website!
.
Amelia,

under this link

https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1110915.html

https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1110915.html

please find very similar problem that I solved couple of days ago at this forum.

It is a TWIN to your problem.

Consider it as your sample and then solve your problem in the same manner.

If you still have questions, post them to the forum or directly to me via the "Thank you" note.

Answer by phillywily(18) (Show Source):
You can put this solution on YOUR website!
Alright. Given that this is an arithmetic sequence, so the difference between the second term and the first term is equal to the difference between the third term and the second term.
Henceforth,
T3 - T2 = T2 - T1
4x+6-2x = 2x-(x-5)
2x+6 = x+5
X=-1
Now we substitute x into the equations.
The first term is x-5, hence
-1-5=-6
T2
= 2x
= 2(-1)
= -2
T3
= 4x+6
= 4(-1)+6
= -4+6
= 2
Hence, the three terms are -6, -2 and 2 respectively.