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What is the explicit rule for the sequence?
- 114, -109, -104, -99,

An= -5n - 109
An= -5n - 119
An= 5n - 119
An= 5n - 109

Respuesta :

eshaanbarkataki

Answer:

5n - 119

Step-by-step explanation:

First, we notice that the sequence is going up by 5, so we could rule out 2 answers: -5n - 109, and -5n -119 (They go by -5). Then all we have to find is the  constant, -119 or -109. Well we could rule out -109 because -114 is included in the sequence, and if we start by -109 and start counting up, we will never get to -114. So, the solution is 5n - 119

We have been given that - 114, -109, -104, -99. the explicit rule for the sequence is 5n - 119.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

[tex]T_n = a + (n-1)d[/tex]

(for all positive integer values of n)

And thus, the common difference is

[tex]T_{n+1} - T_n[/tex]

for all positive integer values of n

We have been given that

- 114, -109, -104, -99,

a = -114

[tex]T_n = a + (n-1)d[/tex]

T = -114 + (n - 1)5

T = 5n - 119

Learn more about arithmetic sequence here:

https://brainly.com/question/3702506

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