Word problem

Question

The first  three  terms  of  an   Arithmetic Progression are ( x + 1 ), ( 4x - 2 ) and ( 6x - 3).If the  last  term  is 18, find x

Answer 1

An Arithmetic Sequence has a common difference:

 

(4x - 2) - (x + 1) = (6x - 3) - (4x - 2)

 

Can you solve for x and answer?

Answer 2

( x + 1 ), ( 4x - 2 ) and ( 6x - 3)

 

As Mark said, if this was an arithmetic progression with these as the first 3 terms then:

(4x-2) - (x+1) = (6x-3) - (4x-2) since there is a common difference:

 

4x - 2 - x - 1 = 6x - 3 - 4x + 2

3x - 3 = 2x - 1

x = 2

 

Your sequence is:  3, 6, 9, 12, 15, 18 and the common difference is 3

Note: We did not need the last term to solve for x