Answer:
The series is 5 , 6 , 7 , 8 , 9 , 10 , 11
Explanation:
* Lets revise the arithmetic series
- In the arithmetic series there is a constant difference between
each two consecutive numbers
- Ex:
# 2 , 5 , 8 , 11 , ………………………. (constant difference is 3)
# 5 , 10 , 15 , 20 , ………………………… (constant difference is 5)
# 12 , 10 , 8 , 6 , …………………………… (constant difference is -2)
* General term (nth term) of an Arithmetic series:
- If the first term is a and the common diffidence is d, then
U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
- So the nth term is Un = a + (n – 1)d, where n is the position of the
number in the series
* Lets solve the problem
- Jeff wants to increase the number of miles he runs each day
∴ He will add the initial value by constant number each day
- He plans on increasing the number of miles he runs a day by 1
∴ The constant value is 1 mile
- On the first day of training, Jeff runs 5 miles
∴ The first value is 5 miles
∴ The series is arithmetic
∵ a = 5 , d = 1
- He do that for the remainder of the week
∵ The week has 7 days
∴ The series has 7 terms
∵ The rule of the series is Un = a + (n - 1)d
∵ a = 5 and d = 1
∴ Un = 5 + (n - 1)(1)
∴ Un = 5 + n - 1
∴ Un = 4 + n ⇒ n is the position of the number
- Substitute n from 1 to 7 to find the series
∴ The series is 5 , 6 , 7 , 8 , 9 , 10 , 11