Add sequences of numbers in the 80's

1. Choose a 2-digit number in the 80's. To add all the80's
   from 80 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 8 (add the carry)  X X _

   Example:

1. If the 2-digit number in the 80's selected is 83:
   (80 + 81 + 82 + 83 + 82 + 81 + 80)
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. 8 x no. of terms: 8 x 7 = 56  5 6 _
5. So the sum of the sequence is 569.

   See the pattern?

1. If the 2-digit number in the 80's selected is 88:
   (80 + 81 + 82 ... + 88 + 87 + ... 83 + 82 + 81 + 80)
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. 8 x no. of terms (+ carry): 8 x 17 + 6
   = 80 + 56 + 6 = 136 + 6 = 42   4 2 _
5. So the sum of the sequence is 1424.