Given that, 6x-1, 3x, and 2x+3 are the first three terms of an A.P. finda) the value of xb) the first term and the common difference.   Hi, I have a question about arithmetic sequenceThe question is  Given that, 6x-1, 3x, and 2x+3 are the first three terms of an A.P. finda) the value of xb) the first term and the common difference.

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The first three terms of the arithmetic progression are,

`6x-1` , `3x ` and `2x+3`

The common difference of an arithmetic progression is the difference between two consecutive terms. If the common difference is d, then, we can write expressions for common difference using the three terms given.

Using first two terms,

`d = 3x - (6x-1) = -3x+1`


Using the second and third terms,

`d = (2x+3) - 3x = -x+3`

 

Butt we know these two expressions are equal, then,

`-3x+1 = -x+3`

`-3x+x = 3-1`

`-2x = 2`

`x = -1`


Therefore `x = -1,`

Then the common difference is,

`-x+3 = -(-1)+3 = 1+3 = 4.`

`d = 4.`

 

The first term is,

`6x-1 = 6(-1) -1 = -6-1=-7`


The common difference is +4 and the first term is -7.

 

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