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What is the 6th term in the sequence described by the following recursive formula?

a1=9
an=an−1−4

A) a6=−7
B) a6=−15
C) a6=−8
D) a6=−11

Respuesta :

grujan50

Answer:

Correct answer is: D) a₆ = - 11

Step-by-step explanation:

Given:

a₁ = 9 and aₙ = aₙ₋₁ - 4

We know it is

a₆ = a₅ + d also it is given a₆ = a₅ - 4

When we equate the right sides of equality we get:

a₅ + d = a₅ - 4 => d = - 4

We also know it is   a₆ = a₁ + 5 d

Now we will find a₆

a₆ = 9 + 5 (-4) = 9 - 20 = - 11

a₆ = - 11

God with you!!!

The sixth term of the sequence will be a₆ = - 11. Then the correct option is D.

What are sequence and series?

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The first term (a₁) is 9 and the nth term will be given as

[tex]\rm a_n = a_{n-1} - 4[/tex]

Then the second term will be

a₂ = a₁ - 4

a₂ = 9 - 4

a₂ = 5

Then the third term will be

a₃ = a₂ - 4

a₃ = 5 - 4

a₃ = 1

Then the fourth term will be

a₄ = a₃ - 4

a₄ = 1 - 4

a₄ = -3

Then the fifth term will be

a₅ = a₄ - 4

a₅ = -3 - 4

a₅ = -7

Then the sixth term will be

a₆ = a₅ - 4

a₆ = -7 - 4

a₆ = - 11

Then the correct option is D.

More about the sequence link is given below.

https://brainly.com/question/21961097

#SPJ2

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