Add sequences of numbers in the 50's

1. Choose a 2-digit number in the 50's. To add all the 50's
   from 50 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 5.   X X _

   Example:

1. If the 2-digit number in the 50's selected is 53:
   (50 + 51 + 52 + 53 + 52 + 51 + 50)
2. Square the 2nd digit of the number: 3 x 3 = 9   _ _ 9
3. No. of terms = 2 x 2nd digit + 1: 2 x 3 + 1 = 7
4. 5 x no. of terms: 5 x 7 = 35  3 5 _
5. So the sum of the sequence is 359.

   See the pattern?

1. If the 2-digit number in the 50's selected is 57:
   (50 + 51 + 52 ... + 57 + 56 + ... 52 + 51 + 50)
2. Square the 2nd digit of the number: 7 x 7 = 49
   (keep carry 4)   _ _ 9
3. No. of terms = 2 x 2nd digit + 1: 2 x 7 + 1 = 15
4. 5 x no. of terms (+ carry): 5 x 15 + 4 = 75 + 4
   = 79   7 9 _
5. So the sum of the sequence is 799.