Caden started exercising by doing 9 push-ups on the first day. Every day, he would do 2 more push-ups than the day before. How many push-ups did he do altogether after 6 days?
| |
Number of
push-ups |
Number of
push-ups |
Total number
of push-ups |
| Day 1 |
9 |
7 + (1 x 2) |
9 |
| Day 2 |
9 + 2 |
7 + (2 x 2) |
9 + 11 |
| Day 3 |
9 + 2 + 2 |
7 + (3 x 2) |
9 + 11 + 13 |
| |
Total number
of push-ups |
Total number
of push-ups |
| Day 1 |
9 |
(1 + 3 + ... + 9) - (1 + 3 + ... + 7)
= 52 - 42
= 9 |
| Day 2 |
9 + 11 |
(1 + 3 + ... + 11) - (1 + 3 + ... + 7)
= 62 - 42
= 20 |
| Day 3 |
9 + 11 + 13 |
(1 + 3 + ... + 13) - (1 + 3 + ... + 7)
= 72 - 42
= 33 |
| Day 6 |
9 + 11 + 13 + 15 + ... + 19 |
(1 + 3 + ... + 19) - (1 + 3 + ... + 7)
= 102 - 42
= 84 |
Formula:
Number of push-ups = 7 + (Day x 2)
Number of push-ups on Day 6 = 7 + (6 x 2) = 19
To find the range of odd numbers not included
= Total number of push-ups on Day 1 - 2
= 9 - 2
= 7
- Range of odd numbers from 1 to 7 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 7
= (7 + 1) ÷ 2
= 4
Number of odd numbers from 1 to 19
= (19 + 1) ÷ 2
= 10
Sum of odd numbers from 1 to 7
= 4
2= 4 x 4
= 16
Sum of odd numbers from 1 to 19
= 10
2 = 10 x 10
= 100
Sum of odd numbers from 9 to 19
= 100 - 16
= 84
Total number of push-ups after 6 days = 84
Answer(s): 84
