We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
608
2
avatar

If the first three terms of an arithmetic progression are (x+3). (3x-10) and (2x+10), find x.

 Feb 9, 2018
 #1
avatar
+1

(x+3)+ (3x-10) + (2x+10) =6x + 3

Sum them up as an arithmetic series:

6x + 3=3/2 *[2*[x+3] + (3-1)*(2x - 13)], solve for x

 

Solve for x:

6 x + 3 = (3 (2 (x + 3) + 2 (2 x - 13)))/2

 

6 x + 3 = (3 (2 x + 6 + 2 (2 x - 13)))/2

 

6 x + 3 = (3 (4 x - 26 + 2 x + 6))/2

 

Grouping like terms, 4 x + 2 x - 26 + 6 = (2 x + 4 x) + (6 - 26):

6 x + 3 = (3 ((2 x + 4 x) + (6 - 26)))/2

 

6 x + 3 = (3 (6 x + (6 - 26)))/2

 

6 x + 3 = (3 (6 x + -20))/2

 

Multiply both sides by 2:

2 (6 x + 3) = (2×3 (6 x - 20))/2

 

(2×3 (6 x - 20))/2 = 2/2×3 (6 x - 20) = 3 (6 x - 20):

2 (6 x + 3) = 3 (6 x - 20)

Expand out terms of the left hand side:

12 x + 6 = 3 (6 x - 20)

 

Expand out terms of the right hand side:

12 x + 6 = 18 x - 60

12x - 18x = -60 - 6

- 6x = - 66

x = -66 / -6

x= 11

 

 

 

 

 

 

 

 

 

 

 

 Feb 9, 2018
edited by Guest  Feb 10, 2018
 #2
avatar+101090 
+1

We have that :

 

(x + 3)  + d  =  (3x - 10)       (1)

 

(3x - 10) + d  = (2x + 10)     (2)

 

Subtract  (2)  from  (1)   and we have

 

( x + 3)  - (3x - 10)   = (3x - 10) - (2x + 10)     simplify

 

-2x + 13   =  x - 20      add 2x, 20 to both sides

 

33   =  3x       divide both sides by 3

 

11  = x

 

 

cool cool cool

 Feb 10, 2018

17 Online Users

avatar
avatar