Question

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? ​

Answer 1

The 19 th term of the sequence is the first term of the sequence having value greater than 1000.

Given that the n-th term of the sequence is given by,

$a_n=3n^2$

Let the p-th term be the first term which have value greater than 1000 in the sequence.

The p-th term of the sequence is, $a_p=3p^2$

According to the condition,

$3p^2 > 1000$

$\Rightarrow p^2 > \frac{1000}{3}$

$\Rightarrow p > +\sqrt{\frac{1000}{3}}$, as number of term cannot be negative so we ignore the negative value of square root here

$\Rightarrow p > 18.25\\\Rightarrow p\geq19$

Hence the first term which has value greater than 1000 is 19 th term of the sequence.

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