hiramtercero10
Answered

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What expression can be used to find the nth term in the sequence 5,7,9, 11,...?

2n - 3

n + 2

n - 3

2n + 3​

Sagot :

absor201

Answer:

The required expression which can be used to find the nth term in the sequence is:

[tex]a_n=2n+3[/tex]

Hence, the fourth option i.e. 2n+3 is the correct option.

Step-by-step explanation:

Given the sequence

5, 7, 9, 11,...

An arithmetic sequence has a constant difference 'd' and is defined by  

[tex]a_n=a_1+\left(n-1\right)d[/tex]

computing the differences of all the adjacent terms

[tex]7-5=2,\:\quad \:9-7=2,\:\quad \:11-9=2[/tex]

The difference between all the adjacent terms is the same and equal to

d = 2

So

  • a₁ = 5
  • d = 2

Thus, the nth term of the sequence is

[tex]a_n=a_1+\left(n-1\right)d[/tex]

substitute a₁ = 5 and d = 2 in the sequence

[tex]a_n=2\left(n-1\right)+5[/tex]

[tex]a_n=2n+3[/tex]

Therefore, the required expression which can be used to find the nth term in the sequence is:

[tex]a_n=2n+3[/tex]

Hence, the fourth option i.e. 2n+3 is the correct option.

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