Owen started exercising by doing 9 star jumps on the first day. Every day, he would do 2 more star jumps than the day before. How many star jumps did he do altogether after 8 days?
| |
Number of
star jumps |
Number of
star jumps |
Total number
of star jumps |
| 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 star jumps |
Total number
of star jumps |
| 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 8 |
9 + 11 + 13 + 15 + ... + 23 |
(1 + 3 + ... + 23) - (1 + 3 + ... + 7)
= 122 - 42
= 128 |
Formula:
Number of star jumps = 7 + (Day x 2)
Number of star jumps on Day 8 = 7 + (8 x 2) = 23
To find the range of odd numbers not included
= Total number of star jumps 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 23
= (23 + 1) ÷ 2
= 12
Sum of odd numbers from 1 to 7
= 4
2= 4 x 4
= 16
Sum of odd numbers from 1 to 23
= 12
2 = 12 x 12
= 144
Sum of odd numbers from 9 to 23
= 144 - 16
= 128
Total number of star jumps after 8 days = 128
Answer(s): 128
