Need help with some math questions! :D

Numero Uno

The first three terms of an arithmetic sequence are given by x, (2x-5), 8.6
Determine the first term and the common difference for the sequence. (Please show work, I don't understand this!)

Numero Dos

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. (Please explain how you did it, I have the answer but I don't understand how to solve it!!)

If you could show work and explain how you did it that'd be great! Thank you!

An arithmetic sequence has a linear nature. Each member is separated from the next by the same thing.

1 3 5 7 ....

3 53 103 153.....

So 2x - 5 - x = 8.6 - (2x - 5)
x - 5 = 13.6 - 2x
3x = 18.6
x = 6.2

That gives us 6.2, 12.4, 18.6

***

Again

(7x - 4) - (5x + 2) = (10x + 6) - (7x - 4)
2x - 6 = 3x + 10
-16 = x

That makes our terms -78, -116, -154

1st question

x , (2x-5) and 8.6 are first three tern of arithmetic sequence
therefore
common difference should be same

8.6 - (2x-5) = 2x-5 -x
8.6 - 2x + 5 = x - 5
3x = 18.6

x = 6.2
2x-5 - x => x-5 => 6.2 - 5 => 1.2

therefore1st term of arithmetic series is 6.2
Common difference is 1.2


2nd question

5x+2 , 7x-4 and 10x+6 are first three tern of arithmetic sequence
therefore
common difference should be same

7x-4 - (5x+2) = 10x+6 - (7x-4)
7x - 4 - 5x -2 = 10x + 6 - 7x +4
2x - 6 = 3x + 10
x = -16

therefore first three terms are 5(-16) + 2 , 7(-16) - 4 and 10(-16) + 6
therefore first three terms are -78 , -116 and -154
here common difference is -38

First term = x
2nd term = x + d -------- d is common difference
x + d = 2x – 5
x = d + 5

3rd term = x + 2d = 8.6
d + 5 + 2d = 8.6
3d = 3.6
d = 3.6/3 = 1.2

then x = 1.2 + 5 = 6.2
so terms
x, (2x – 5), 8.6
are
6.2, 7.4, 8.6

if we add 1 to any number we get next number d = 1
so 5x + 2 + d = 7x – 4
2x = d + 6
d = 2x – 6
similarly
7x – 4 + 1 = 10x + 6
3x = – 3
10x + 6 = – 24 --------- 3rd term
7x – 4 = – 25 --------- 2nd term

first term = – 26
but 5x + 2 = – 13 not – 26
it should be 8x – 2
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the terms are not consecutive