Respuesta :

tamaraqueenplace

Step-by-step explanation:

these number grow by four every time

Y N

1 -2

2 - 6

3- 10

4- 14

N= 4× Y

2= 4 × 1

2= 4

2-4= -2

4× N + -2

4 × 42+ -2

168- -2= 166

Therefore the term of 166 will be 42.

The series of numbers are increasing by a constant amount each term,

making it an arithmetic series or progression.

  • The term number that has a value of 166 is the 42nd term

Reasons:

  • The first term of the given sequence, a₁ = 2

The difference between the terms are;

  • 6 - 2 = 10 - 6 = 14 - 10 = 4

Therefore;

  • Each subsequent term has a constant or common difference of , d = 4

  • The sequence is an arithmetic progression, and the value of the nth term of the sequence is therefore;

  • aₙ  = a₁ + (n - 1)·d

Where;

n = The nth term of the sequence

Which gives;

aₓ  = 2 + (n - 1)·4 = 166

  • (n - 1)·4 = 166 - 2 = 164

[tex]n - 1 = \dfrac{164}{4} = 41[/tex]

Which gives;

n = 41 + 1 = 42

  • n = 42

Therefore;

  • 166 is the 42nd term of the sequence

Learn more here:

https://brainly.com/question/24064200

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