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 From B. Lee Clay

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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 × 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 × 3 = 9 `  _ _ 9`
3. No. of terms = 2 × 2nd digit + 1: 2 × 3 + 1 = 7
4. 5 × no. of terms: 5 × 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 × 7 = 49
(keep carry 4) `  _ _ 9`
3. No. of terms = 2 × 2nd digit + 1: 2 × 7 + 1 = 15
4. 5 × no. of terms (+ carry): 5 × 15 + 4 = 75 + 4
= 79 `  7 9 _`
5. So the sum of the sequence is 799.