Series series questions If S12 / 4 = S9 / 3 + 2 is known as the arithmetic sequence, the tolerance of the sequence is

Series series questions If S12 / 4 = S9 / 3 + 2 is known as the arithmetic sequence, the tolerance of the sequence is

Let the tolerance be d
S12/4 =S9 /3 +2
(12a1+66d)/4=(9a1+36d)/3 +2
It's time to tidy up
(3/2)d=-2
d=-4/3

The problem of sequence,
Proof: the arithmetic sequence an = (2 / 3) ^ n-2, any three items can not form the arithmetic sequence

First floor did not pay attention to "arbitrary" two words, the following is my solution
Let ax, ay, AZ satisfy the condition, and let xaz > 0,
So there is 2ay = ax + AZ
2 * (2 / 3) ^ Y-2 = (2 / 3) ^ X-2 + (2 / 3) ^ Z-2 multiply both sides by (3 ^ z) / (2 ^ x)
2*2^(y-x)*3^(z-y)=3^(z-y)+2^(z-x)
Even number on the left
The first term on the right is odd, and the second term is even, so the whole is odd
Come to a contradiction
So it is proved

Find the rules and fill in the blanks. 625125,25, (), (). 2,6,12,20, (), ()

5 1 divided by 5
+4 6 8 so the next one is 30 32