During one of their routines, the Longsboro High School marching band members line up in a succession of L-shaped formations. The first 4 formations, numbers 1 through 4, are shown below, with each dot representing a band member. The pattern demonstrated by the addition of band members in the first 4 formations continues through each successive L-shaped formation in the routine. Which of the following equations gives the relationship between \(n\), the formation number, and \(b\), the number of band members in that formation?

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The number of band members is the sequence:

$$ 5, 7, 9, 11... $$

This is an arithmetic sequence with first term 5 and difference 2

$$ a_n = a_1 + d(n-1) $$ $$ a_n = 5 + 2(n-1) $$ $$ a_n=5+2n-2 $$ $$ a_n = 2n+3 $$

We can simply plug in values into the equations. For example, the equation needs to work for \(n=1\) and \(b=5\). Make sure to test multiple situations until one one answer choice works.