numbers in sequence and series

I am told the first $\displaystyle n$ term of a sequence is $\displaystyle n^{2}$, and told to find the $\displaystyle 10^{th}$ term in the sequence, and the smallest value of $\displaystyle r$ for which the $\displaystyle r^{th}$ term exceeds 10 000. By using the left side of the formula

$\displaystyle

sum_{r=1}^n r^2 = \frac{1}{6} n (n+1)(2n+1)$ I think I can find the tenth term but I am unsure how to find the smallest value of $\displaystyle r$ for which the $\displaystyle r^{th}$ term exceeds 10 000.

any hints or guidance would be well met. Thankyou.

numbers in sequence and series

*Sorry, here is the question as given:*

*The sum first http://www.mathhelpforum.com/math-he...b31363a1-1.gif term of a sequence is http://www.mathhelpforum.com/math-he...392c01c6-1.gif.Find the http://www.mathhelpforum.com/math-he...ea85c378-1.gif term in the sequence, and the smallest value of http://www.mathhelpforum.com/math-he...9b3dc231-1.gif for which the http://www.mathhelpforum.com/math-he...bd3aad87-1.gif term exceeds 10 000.*

*My idea(s):*

*By using the left side of the formula *

*http://www.mathhelpforum.com/math-he...951c1417-1.gif I think I can find the tenth term but I am unsure how to find the smallest value of http://www.mathhelpforum.com/math-he...9b3dc231-1.gif for which the http://www.mathhelpforum.com/math-he...bd3aad87-1.gif term exceeds 10 000.*

*(forgive me for any inconvenience)*

*any hints or guidance would be well met. Thankyou.*