You could be asking two different things, but most likely the first.
"What is the next number in the sequence 972, 324, 108?"
To determine the next number in a sequence you need to define the rule of the sequence first. The rule is the relationship between two of the terms. Let's compare the terms.
972:324=3:1
324:108=3:1
972 is three times the value of 324. 324 is three times the value of 108. This means that each number is one-third the size of the previous number. Label the next number X.
X=108/3
X=36
The sequence is 972, 324, 108, 36.
"What is the next number in the sequence 972324108?"
In math, a sequence is a list of numbers in a special order. Multiple numbers are needed to created a sequence. 972324108 is only one number and therefore is not a sequence.
If you are asking what number comes after 972324108, 972324109 comes after it.
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The sequence is taking half of the number and adding it to that number, 3/2 = 1.5, 3 + 1.5 = 4.5, the next number in the sequence is 15.1875