Add sequences of numbers in the 30's

1. Choose a 2-digit number in the 30's. To add all the 30's
   from 30 up through this number and down from it:
2. Square the 2nd digit of the number
   (keep the carry)   _ _ X
3. The number of terms is 2 x the 2nd digit + 1.
4. Multiply the number of terms by 3 (+ carry)  X X _

   Example:

1. If the 2-digit number in the 30's selected is 34:
   (30 + 31 + 32 + 33 + 34 + 33 + 32 + 31 + 30)
2. Square the 2nd digit of the number:
   4 x 4 = 16 (keep carry 1)   _ _ 6
3. No. of terms = 2 x 2nd digit + 1:
   2 x 4 + 1 = 9
4. 3 x no. of terms: 3 x 9 + 1 = 28   2 8 _
5. So the sum of the sequence is 286.

   See the pattern?

1. If the 2-digit number in the 30's selected is 38:
   (30 + 31 + 32 + ... + 38 + 37 + ... 32 + 31 + 30)
2. Square the 2nd digit of the number:
   8 x 8 = 64 (keep carry 6)   _ _ 4
3. No. of terms = 2 x 2nd digit + 1:
   2 x 8 + 1 = 17
4. 3 x no. of terms: 3 x 17 + 6 = 51 + 6 = 57  5 7 _
5. So the sum of the sequence is 574.