Question

Karen counts the number of high jumps she does at the end of each week. At the end of the first week Karen completes 50 high jumps, the end of the second week, she completes 62 high jumps and at the end of the third week she completes 74 high jumps. Which of the following can be used to determine the number of high jumps that Karen completes at the end of the nth week? Select all that apply.

Answer 1

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:

$a_{n}$ = 12 n + 38 ⇒ A

$a_{n}$ = 50 + (n - 1)12 ⇒ C

$a_{n}$ = $a_{n-1}$ + 12,  $a_{1}$ = 50 ⇒ E

Step-by-step explanation:

The recursive formula of the nth term of the arithmetic sequence is:  

$a_{1}$ = first term;  $a_{n}$ = $a_{n-1}$ + d, where d is the common difference between each two consecutive terms

The explicit formula of the nth term of the arithmetic sequence is:

$a_{n}$ = 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 $a_{1}$ = 50;  $a_{n}$ = $a_{n-1}$ + 12 ⇒ E

∴ The explicit formula is $a_{n}$ = 50 + (n - 1)12 ⇒ C

Lets simplify the explicit formula

∵ $a_{n}$ = 50 + (n - 1)12

- Multiply 12 by (n - 1)

∴ $a_{n}$ = 50 + 12 n - 12

- Add the like terms

∴ $a_{n}$ = 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:

$a_{n}$ = 12 n + 38 ⇒ A

$a_{n}$ = 50 + (n - 1)12 ⇒ C

$a_{n}$ = $a_{n-1}$ + 12,  $a_{1}$ = 50 ⇒ E