# Thread: numbers in sequence and series

1. ## 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.

2. Originally Posted by riptorn70
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.
Post the question exactly as it's written please.

3. ## numbers in sequence and series

Sorry, here is the question as given:
The sum first term of a sequence is .Find the term in the sequence, and the smallest value of for which the term exceeds 10 000.

My idea(s):

By using the left side of the formula
I think I can find the tenth term but I am unsure how to find the smallest value of for which the term exceeds 10 000.

(forgive me for any inconvenience)
any hints or guidance would be well met. Thankyou.

4. Originally Posted by riptorn70
Sorry, here is the question as given:
The sum first term of a sequence is .Find the term in the sequence, and the smallest value of for which the term exceeds 10 000.

My idea(s):

By using the left side of the formula
I think I can find the tenth term but I am unsure how to find the smallest value of for which the term exceeds 10 000.

(forgive me for any inconvenience)
any hints or guidance would be well met. Thankyou.
The sum of the first n odd numbers is n^2 .....

This sum is an arithmetic series with first term equal to 1 and the common difference equal to 2.

5. Thankyou dearly for the hint.