Add sequences of numbers in the 40's

1. Choose a 2-digit number in the 40's. To add all the 40's
   from 40 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 4 (+ carry)    X X _

   Example:

1. If the 2-digit number in the 40's selected is 43:
   (40 + 41 + 42 + 43 + 42 + 41 + 40)
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. 4 x no. of terms: 4 x 7 = 28   2 8 _
5. So the sum of the sequence is 289.

   See the pattern?

1. If the 2-digit number in the 40's selected is 48:
   (40 + 41 + 42 + ... + 48 + 47 + ... 42 + 41 + 40)
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. 4 x no. of terms: 4 x 17 + 6 = 40 + 28 + 6 =
   68 + 6 = 74   7 4 _
5. So the sum of the sequence is 744.