the next are and I will let someone else reveal the third
In this case look at the ratios between each consecutive numbers. For the next term consider the relationship between the previous two ratios.
I was playing around to find a number pattern so I started with pascals triangle.
then I added up each row, but not all rows. I chose a row correlating to a financing number subtracted by 1.
But I wanted the sum so.
While your method works yes (although I did not think of it)
It does not explain the first term, only all after.
So, you're answers work but are technically incorrect.