To make [tex]\( a \)[/tex] the subject of the formula [tex]\( S = \frac{n}{2} \left[ 2a + (n-1)d \right] \)[/tex], follow these steps:
1. Isolate the fraction involving [tex]\( a \)[/tex]:
[tex]\[
S = \frac{n}{2} \left( 2a + (n-1)d \right)
\][/tex]
2. Multiply both sides by 2 to eliminate the denominator on the right side:
[tex]\[
2S = n \left( 2a + (n-1)d \right)
\][/tex]
3. Divide both sides by [tex]\( n \)[/tex] to isolate the term containing [tex]\( a \)[/tex] on the right side:
[tex]\[
\frac{2S}{n} = 2a + (n-1)d
\][/tex]
4. Subtract [tex]\( (n-1)d \)[/tex] from both sides to isolate the term [tex]\( 2a \)[/tex]:
[tex]\[
\frac{2S}{n} - (n-1)d = 2a
\][/tex]
5. Divide both sides by 2 to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{1}{2} \left( \frac{2S}{n} - (n-1)d \right)
\][/tex]
So, [tex]\( a \)[/tex] is:
[tex]\[
a = \frac{1}{2} \left( \frac{2S}{n} - (n-1)d \right)
\][/tex]
This can be alternatively written as:
[tex]\[
a = \frac{(2S / n) - (n-1)d}{2}
\][/tex]
