Question

PLEASE HELP ME WITH THESE 2 QUESTIONS YOU GUYS, I AM TRYING TO PASS MATH CLASS. PLEASE. please. I AM GIVING 30 PTS FOR THIS. PLEASE.

1. Write the recursive formula and the explicit formula for the sequence {-15,-7,1,9, 17,...}. Show all work.

2. In a paragraph, write which formula, recursive or explicit, is easiest for you to use when finding the 10th term in a sequence. Explain your reasoning in complete sentences.

Answer 1

Recursive formula:
`a_(n)` =
`a_(n-1)` + d ; where
`a_(n-1)` is the previous term, d is the difference, n is the term.

`a_(n)` =
`a_(n-1)` + 8

Explicit formula:
`a_(n)` = a₁ + d(n - 1) ; where a₁ is the first term, d is the difference, n is the term.

`a_(n)` = -15 + 8(n - 1)

= -15 + 8n - 8

= 8n - 23

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Using Recursive formula: a₁₀ = a₉ + 8

a₁ = -15

a₂ = -15 + 8 = -7

a₃ = -7 + 8 + 1

a₄ = 1 + 8 = 9

a₅ = 9 + 8 = 17

a₆ = 17 + 8 = 25

a₇ = 25 + 8 = 33

a₈ = 33 + 8 = 41

a₉ = 41 + 8 = 49

a₁₀ = 49 + 8 = 57

Using Explicit formula: a₁₀ = 8(10) - 23

a₁₀ = 80 - 23

a₁₀ = 57

Answer 2

Explicit Formula

Just in case you don't know what this is, the explicit formula is the formula that solves for any term in the series without necessarily knowing what came before the term you are solving.

Givens

d = t_(n + 1) - t_n You can take any term and the next term for this part of the formula

d = t_3 - t_2

t_3 = 1

t_2 = -7

d = 1 - - 7 = 8

a = -15

Formula

t_n = a + (n - 1)*d

t_n = -15 + (n - 1)*8

For example find the 5th term.

t_5 = - 15 + (5 - 1)*8

t_5 = - 15 + 4 *8

t_5 = -15 + 32

t_5 = 17 Which is what you have.

Recursive Formula

Computers really like this formula. They use it in what is called a subroutine and they pass values from one part of the program to a subroutine which evaluates the given and sends the result back. I'm telling you all this so you see why you are doing it. The disadvantage of it for humans is that you must know the preceding term to use the recursive formula.

Formula

t_n = t_(n - 1) + d

Example

t_6 = t_(6 - 1) + d

t_6 = t_5 + 8

t_6 = 17 + 8

t_6 = 25

You can check this by using the explicit formula.