Jenson started exercising by doing 9 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 12 days?
|
Number of planks |
Number of planks |
Total number of planks |
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 planks |
Total number of planks |
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 12 |
9 + 11 + 13 + 15 + ... + 31 |
(1 + 3 + ... + 31) - (1 + 3 + ... + 7) = 162 - 42 = 240 |
Formula:
Number of planks = 7 + (Day x 2)
Number of planks on Day 12 = 7 + (12 x 2) = 31
To find the range of odd numbers not included
= Total number of planks 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 31
= (31 + 1) ÷ 2
= 16
Sum of odd numbers from 1 to 7
= 4
2= 4 x 4
= 16
Sum of odd numbers from 1 to 31
= 16
2 = 16 x 16
= 256
Sum of odd numbers from 9 to 31
= 256 - 16
= 240
Total number of planks after 12 days = 240
Answer(s): 240