Question

The nth term of a sequence is given by 3n^2.

What is the position of the term in the sequence that is the first one with a value greater than 1000?

Answer 1

Given: The nth term of a sequence is given by 3n^23n

2

.

let a_na

n

be the nth term.

then a_n=3n^2a

n

=3n

2

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

Then \begin{gathered}a_m > 1000\\\Rightarrow3m^2 > 1000\\\Rightarrow\ m^2 > \frac{1000}{3}\\\Rightarrow\ m^2 > 333.333\\\Rightarrow\ m > 18.2573\\\Rightarrow\ m=19\end{gathered}

a

m

>1000

⇒3m

2

>1000

⇒ m

2

>

3

1000

⇒ m

2

>333.333

⇒ m>18.2573

⇒ m=19

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

Now, a_{19}=3(19)^2=3(361)=1083a

19

=3(19)

2

=3(361)=1083

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

Answer 2

I hope this will help you dear..

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