Trying to solve for x, pattern 13, 40, 85, 148, x.can't get the equation....help

Question

set              1     2       3       4         5

outcome    13   40      85    148       x

 

solve X

what would x be at 10

what would x be at the Nth set

Answer 1

Series 13 40 85 148  229

 1st diff   27 45 63  81     

 2nd diff      18 18 18

There's a pattern because the 2nd differences appear to be the same.

Let's take 4 off each of the terms in the series:

9, 36, 81, 144, which are 1×9, 4×9, 9×9, 16×9.

1, 4, 9, 16 are the squares of the natural numbers. Also 229-4=225=25×9.

The formula for the series is 9n²+4 where n=1, 2, 3, 4, ...

When n=10, the term is 904, because 10²=100. So x=904.

For N, x=9N²+4.