Jeremy started exercising by doing 9 sit-ups on the first day. Every day, he would do 2 more sit-ups than the day before. How many sit-ups did he do altogether after 7 days?
|
Number of sit-ups |
Number of sit-ups |
Total number of sit-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 sit-ups |
Total number of sit-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 7 |
9 + 11 + 13 + 15 + ... + 21 |
(1 + 3 + ... + 21) - (1 + 3 + ... + 7) = 112 - 42 = 105 |
Formula:
Number of sit-ups = 7 + (Day x 2)
Number of sit-ups on Day 7 = 7 + (7 x 2) = 21
To find the range of odd numbers not included
= Total number of sit-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 21
= (21 + 1) ÷ 2
= 11
Sum of odd numbers from 1 to 7
= 4
2= 4 x 4
= 16
Sum of odd numbers from 1 to 21
= 11
2 = 11 x 11
= 121
Sum of odd numbers from 9 to 21
= 121 - 16
= 105
Total number of sit-ups after 7 days = 105
Answer(s): 105