Study the number pattern.
- In 56 what is the sum of the digits in the ones and tens place?
- What is the sum of the last three digits in 511?
- What is the sum of the last four digits in 558?
| Pattern |
|
|
| 51 |
5 |
= 5 |
| 52 |
5 x 5 |
= 25 |
| 53 |
5 x 5 x 5 |
= 125 |
| 54 |
5 x 5 x 5 x 5 |
= 625 |
| 55 |
5 x 5 x 5 x 5 x 5 |
= 3125 |
| 56 |
5 x 5 x 5 x 5 x 5 x 5 |
= 15625 |
| 57 |
5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 78125 |
| 58 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 390625 |
| 59 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 1953125 |
| 510 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 9765625 |
| 511 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 48828125 |
| 512 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 244140625 |
| 513 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 1220703125 |
| 514 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 6103515625 |
| 515 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 30517578125 |
(a)
Sum of the last two digits is 2 and 5.
Sum of digits in ones and tens place in 5
6 = 2 + 5
= 7
(b)
Last three digits in odd-numbered powers is
1, 2 and
5.
Sum of the last three digits in 5
11 = 1 + 2 + 5
= 8
(c)
For even-numbered powers from 5
6 onwards
Formula:
(1) If even-numbered powers ÷ 2 has an odd-numbered quotient, the last four digits is
5, 6, 2 and
5.
(2) If even-numbered powers ÷ 2 has an even-numbered quotient, the last four digits is
0, 6, 2 and
5.
58 ÷ 4 = 14 r 2
Since the remainder is 2, the sum of the last four digits in 5
58 = 5 + 6 + 2 + 5
= 18
Answer(s): (a) 7; (b) 8; (c) 18
