Carl started exercising by doing 7 planks on the first day. Every day, he would do 2 more planks than the day before. How many planks did he do altogether after 11 days?
| |
Number of
planks |
Number of
planks |
Total number
of planks |
| 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 planks |
Total number
of planks |
| 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 11 |
7 + 9 + 11 + 13 + ... + 27 |
(1 + 3 + ... + 27) - (1 + 3 + ... + 5)
= 142 - 32
= 187 |
Formula:
Number of planks = 5 + (Day x 2)
Number of planks on Day 11 = 5 + (11 x 2) = 27
To find the range of odd numbers not included
= Total number of planks 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 27
= (27 + 1) ÷ 2
= 14
Sum of odd numbers from 1 to 5
= 3
2= 3 x 3
= 9
Sum of odd numbers from 1 to 27
= 14
2 = 14 x 14
= 196
Sum of odd numbers from 7 to 27
= 196 - 9
= 187
Total number of planks after 11 days = 187
Answer(s): 187
