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The nth term of a sequence is given by 3n2. What is the position of the term in the sequence that is the first one with a value greater than 1000

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JeanaShupp

Answer: 19


Step-by-step explanation:

Given: The nth term of a sequence is given by [tex]3n^2[/tex].

let [tex]a_n[/tex] be the nth term.

then [tex]a_n=3n^2[/tex]

Let m be the term which is the first one with a value greater than 1000.

Then [tex]a_m>1000\\\Rightarrow3m^2>1000\\\Rightarrow\ m^2>\frac{1000}{3}\\\Rightarrow\ m^2>333.333\\\Rightarrow\ m>18.2573\\\Rightarrow\ m=19[/tex]

Thus, 19 th term is the first one with a value greater than 1000 the sequence that is

Now, [tex]a_{19}=3(19)^2=3(361)=1083[/tex]

hence, the position of 1083 is 19 in the sequence that is the first one with a value greater than 1000

aksnkj

19th term of the sequence will be greater than 1000 and it will be the first to be more than 1000.

Given information:

The nth term of a sequence is given by

[tex]3 {n}^{2} [/tex]

It is required to find the position of the term in the sequence that is the first one with a value greater than 1000.

The term should be greater than 1000.

So, the value of n or the position can be found as,

[tex]a_n=3 {n}^{2} \\ 3 {n}^{2} > 1000 \\ n > \sqrt{ \frac{1000}{3} } \\ n > 18.25[/tex]

So, the value of n should be greater than 18.25 which should be 19.

Therefore, 19th term of the sequence will be greater than 1000 and it will be the first to be more than 1000.

For more details, refer to the link:

https://brainly.com/question/16764618

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