# Find the next number in the following sequence [Mind bender]

I came across this sequence in the paper:

109080, 12123, 1350, 153, ?

What could be the next number? And what is the pattern that connects these numbers?

Dividing a term by the next term leads to a number which consecutively decreases from 8.99 for the first term to 8.8 for the third term Is that of any use?

If you compute one term minus nine times the next one, you always get $$-27$$. In other words: $$x_{i+1}=\frac{x_i+27}9 \,\, \left(\text{or \frac{x_i}9+3}\right)$$ Note that $$20$$ is the last integer in this sequence, because it falls under $$9$$ at the next step.
• Or $x_n = (133*9^n+27)/8$ for $n=4,3,2,1,0$ – Florian F Aug 13 '19 at 20:36