Howard started exercising by doing 7 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 15 days?
| |
Number of
star jumps |
Number of
star jumps |
Total number
of star jumps |
| 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 star jumps |
Total number
of star jumps |
| 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 15 |
7 + 9 + 11 + 13 + ... + 35 |
(1 + 3 + ... + 35) - (1 + 3 + ... + 5)
= 182 - 32
= 315 |
Formula:
Number of star jumps = 5 + (Day x 2)
Number of star jumps on Day 15 = 5 + (15 x 2) = 35
To find the range of odd numbers not included
= Total number of star jumps 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 35
= (35 + 1) ÷ 2
= 18
Sum of odd numbers from 1 to 5
= 3
2= 3 x 3
= 9
Sum of odd numbers from 1 to 35
= 18
2 = 18 x 18
= 324
Sum of odd numbers from 7 to 35
= 324 - 9
= 315
Total number of star jumps after 15 days = 315
Answer(s): 315
