Discover new information and insights with the help of IDNLearn.com. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.

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 :

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.