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If the first term of an arithmetic sequence equals the third minus the second, and the fourth term is , what is the first term?

 Feb 20, 2021
 #1
avatar+118069 
0

What is  the  4th term  ???

 

cool cool cool

 Feb 20, 2021
 #2
avatar+229 
0

Oops sorry, the fourth term is 8!

 Feb 20, 2021
 #3
avatar+118069 
+1

Let's see

 

Let  the  first  term  =   a

 

Second  term  = a  +  d          where  d is the common difference

 

Third term  =    a  +  2d

 

Fourth term  =  a  + 3d  =  8

 

Third term   - Second  term  =   First  term

(a   + 2d)  - ( a + d)  =  a

2d -  d =   a

d  = a

 

So

a + 3d  =  8         so

d   + 3d   =  8

4d    = 8

d =  2  =   1st  term =  a

 

Proof

Series  is      2 , 4  , 6 ,  8

6 - 4  =   2

 

cool cool cool

 Feb 20, 2021

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