Use the indicated formula to find the sum.
-Use $S = n ^ { 2 }$ to find the sum of $1 + 3 + 5 + \ldots + 601$.
A) 90,602
B) 90,601
C) 90,600
D) 90,000

Question

Quizplus · Accepted Answer

The formula $S = n^2$ is used to find the sum of the first $n$ odd numbers. To find $n$, note that the sequence starts at 1 and ends at 601, with a common difference of 2 (since it's a sequence of odd numbers). The nth term of an arithmetic sequence is given by $a_n = a_1 + (n-1)d$, where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. Setting $a_n = 601$, $a_1 = 1$, and $d = 2$, we solve for $n$: $601 = 1 + (n-1)2$, which simplifies to $600 = 2(n-1)$, so $n = 301$. Using the given formula $S = n^2$, the sum is $301^2 = 90601$.

Use the Indicated Formula to Find the Sum S=n2S = n ^ { 2 }S=n2

Use the Indicated Formula to Find the Sum $S = n ^ { 2 }$