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

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.
RELATED QUESTIONS
Hello Online Tutors! Here's my question: If a5=100 and a11=10 are the two terms of an... (answered by ikleyn)
2x-4;x+5 and 3x-1 are the first three terms of an arithmetic sequence.(I) show that x=5... (answered by ikleyn)
The terms 5 + x, 8, and 1 + 2x are consecutive terms in an arithmetic sequence. Determine (answered by MathLover1,josgarithmetic)
If the first three terms in an arithmetic progression are (x+3), (3x-10) and (2x+10),... (answered by Boreal)
If the first three terms of an arithmetic sequence are (2x+1,4x+2,10x-1,...), what is the (answered by mayank)
the first three terms of an arithmetic projection are x,2x+1 and 5x+1.find x and the sum... (answered by ikleyn)
Three numbers form an arithmetic sequence. The first term minus the third term is 8. When (answered by htmentor)
The first and the last term of an arithmetic progression are -0.5 and 140.5 respectively. (answered by math_tutor2020,greenestamps,Edwin McCravy,MathTherapy)
What are the first three terms if the 11th term of an arithmetic sequence is 60 and the... (answered by Edwin McCravy)