A Tricky Sequence

The technique used here is: "Reverse the digits and add"

$\Large{ 12+21=33 \\ 33+33=66 \\ 66+66=132 \\ 132+231=363 \\ 363+363=\boxed{726}}$

We can also find it by multiplying each no by 11.
The product is the third number from it.
12 * 11=132
33 * 11=363
66 * 11=726

my way was probably just luck but 12*2.75 = 33

33*2 = 66

66*2 = 132

132*2.75 = 363

363*2 = 726

so basically you multiply the first time by 2.75 then you multiply the next 2 numbers by 2 and you repeat the pattern

Given no + reversing no =2nd no., 2nd no = reversing no = 3rdno. Thus 363 + 363 = 726

First number = 12

Second number = (1+2) * 10 + (1+2) = 33

Third number = (3+3) * 10 + (3+3) = 66

Forth number = (6+6) * 10 + (6+6) = 132

Fifth number = (1+32) * 10 + (1+32) = 363

Sixth number = (3+63) * 10 + (3+63) = 726

Answer = 726

Follow the steps of algorithm 196. The algorithm says that if you reverse a number and add it to the original number, it is the fastest method to produce palindromic numbers. The name comes because this stage hasn't been reached for the number 196 ever after iterating the above steps a million of times.

I'm quite impressed with the number of ways to solve this!

I thought the pattern was:

Times by three, detract three

Times by two three times

Times by three and subtract thirty three...

times by two thirty three times

So on

But, all patterns are valid!

Add the reverse digits of each number to get the next one. So 12 + 21, etc.

12*1 = 12

33*1 = 33

66*1 = 66

12*11 = 132

33*11= 363

66*11 = 726

One can also use an interesting formula:

Double when digits are only 3s or 6s, otherwise, multiply by 3 and subtract 3.

However, this only work for the first few numbers, failing for 726+627=1353