May someone please help out

CHiMER4

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Aug 2, 2021
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If the following terms make a linear sequence.
Compute the value of n.

(-4n/3)+6 ; (-n/3)+7 ; (-n/3)+3;...

I worked out the difference between term2 and term1 and I got n+1,
For the difference between terms 2 and 3, I got an answer of -4

I got stuck at this point as I'm not even sure if my previous steps/attempts are correct.
 
What do you know about the differences for the terms to be linear?
 
If the following terms make a linear sequence.
Compute the value of n.

(-4n/3)+6 ; (-n/3)+7 ; (-n/3)+3;...

I worked out the difference between term2 and term1 and I got n+1,
For the difference between terms 2 and 3, I got an answer of -4

I got stuck at this point as I'm not even sure if my previous steps/attempts are correct.
Note that: 2a_{n}=a_{n-1}+a_{n+1}
-n/3 + 7 = (-4n/3 +6 + -n/3 +3)/2

-2n/3 + 14 = -5n/3 +9

5 = -n

n = -5

check

(-4n/3 +6 + -n/3 +3)/2 = (20/3 + 6 + 5/3 +3)/2 = (25/3 +9)/2 = 52/6 = 26/3

-n/3 + 7 = 5/3 +7 = 26/3 ....................................................checks
 
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