Luke started exercising by doing 7 squats on the first day. Every day, he would do 2 more squats than the day before. How many squats did he do altogether after 10 days?
| |
Number of
squats |
Number of
squats |
Total number
of squats |
| Day 1 |
7 |
5 + (1 x 2) |
7 |
| Day 2 |
7 + 2 |
5 + (2 x 2) |
7 + 9 |
| Day 3 |
7 + 2 + 2 |
5 + (3 x 2) |
7 + 9 + 11 |
| |
Total number
of squats |
Total number
of squats |
| Day 1 |
7 |
(1 + 3 + ... + 7) - (1 + 3 + ... + 5)
= 42 - 32
= 7 |
| Day 2 |
7 + 9 |
(1 + 3 + ... + 9) - (1 + 3 + ... + 5)
= 52 - 32
= 16 |
| Day 3 |
7 + 9 + 11 |
(1 + 3 + ... + 11) - (1 + 3 + ... + 5)
= 62 - 32
= 27 |
| Day 10 |
7 + 9 + 11 + 13 + ... + 25 |
(1 + 3 + ... + 25) - (1 + 3 + ... + 5)
= 132 - 32
= 160 |
Formula:
Number of squats = 5 + (Day x 2)
Number of squats on Day 10 = 5 + (10 x 2) = 25
To find the range of odd numbers not included
= Total number of squats on Day 1 - 2
= 7 - 2
= 5
- Range of odd numbers from 1 to 5 are not counted.
Formula:
To find the number of odd numbers in a range starting from 1 to the last digit
= (Last digit + 1) ÷ 2
Number of odd numbers from 1 to 5
= (5 + 1) ÷ 2
= 3
Number of odd numbers from 1 to 25
= (25 + 1) ÷ 2
= 13
Sum of odd numbers from 1 to 5
= 3
2= 3 x 3
= 9
Sum of odd numbers from 1 to 25
= 13
2 = 13 x 13
= 169
Sum of odd numbers from 7 to 25
= 169 - 9
= 160
Total number of squats after 10 days = 160
Answer(s): 160
