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In an arithmetic sequence, the sixth term is twice the third term and the 30th term is 60. Find the common difference

 Feb 1, 2021
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60 =   a  +  d (30-1)

60  = a  + 29d        ⇒  a =  60  -29d     (1)

 

3rd term  =  a + 2d

The  sixth  term  =   a +  5d

 

And  we  know  that

 

2(a + 2d)   =  a + 5d          sub (1)  into this

 

2  ( 60 - 29d + 2d)  = 60  - 29d + 5d

 

2 ( 60  - 27d)  = 60  - 24d

 

120  - 54d  = 60  - 24d

 

120 - 60  =   54d - 24d

 

60  =  30d

 

d =  60  / 30     =  2

 

 

cool cool cool

 Feb 1, 2021

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