Answer:
The nth formula can be used to determine the number of high jumps that Karen completes at the end of the nth week are:
= 12 n + 38 ⇒ A
= 50 + (n - 1)12 ⇒ C
= + 12, = 50 ⇒ E
Step-by-step explanation:
The recursive formula of the nth term of the arithmetic sequence is:
= first term; = + d, where d is the common difference between each two consecutive terms
The explicit formula of the nth term of the arithmetic sequence is:
= a + (n - 1)d, where n is the position of the term
∵ Karen completes 50 high jumps at the end of the 1st week
∵ She completes 62 high jumps at the end of the 2nd week
∵ She completes 74 high jumps at the end of the 3rd week
∵ 62 - 50 = 12 and 74 - 62 = 12
- There is a constant difference between each 2 consecutive terms
∴ The numbers of her high jumps formed an arithmetic sequence
∵ The first term is 50
∴ a = 50
∵ The constant difference is 12
∴ d = 12
∴ The recursive formula is = 50; = + 12 ⇒ E
∴ The explicit formula is = 50 + (n - 1)12 ⇒ C
Lets simplify the explicit formula
∵ = 50 + (n - 1)12
- Multiply 12 by (n - 1)
∴ = 50 + 12 n - 12
- Add the like terms
∴ = 12 n + 38 ⇒ A
The nth formula can be used to determine the number of high jumps that Karen completes at the end of the nth week are:
= 12 n + 38 ⇒ A
= 50 + (n - 1)12 ⇒ C
= + 12, = 50 ⇒ E