# numbers in sequence and series

• November 1st 2008, 08:50 PM
riptorn70
numbers in sequence and series
I am told the first $n$ term of a sequence is $n^{2}$, and told to find the $10^{th}$ term in the sequence, and the smallest value of $r$ for which the $r^{th}$ term exceeds 10 000. By using the left side of the formula
$
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 $r$ for which the $r^{th}$ term exceeds 10 000.
any hints or guidance would be well met. Thankyou.
• November 1st 2008, 08:55 PM
mr fantastic
Quote:

Originally Posted by riptorn70
I am told the first $n$ term of a sequence is $n^{2}$, and told to find the $10^{th}$ term in the sequence, and the smallest value of $r$ for which the $r^{th}$ term exceeds 10 000. By using the left side of the formula
$
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 $r$ for which the $r^{th}$ term exceeds 10 000.
any hints or guidance would be well met. Thankyou.

Post the question exactly as it's written please.
• November 1st 2008, 09:44 PM
riptorn70
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.
• November 1st 2008, 09:58 PM
mr fantastic
Quote:

Originally Posted by riptorn70
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.

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.
• November 2nd 2008, 01:59 AM
riptorn70
Thankyou dearly for the hint.