Answer:
d = [tex]\frac{2S-2an}{n(n-1)}[/tex]
Step-by-step explanation:
Given
S = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ]
Multiply both sides by 2 to clear the fraction
2S = n [ 2a + (n - 1)d ] ← distribute the bracket by n
2S = 2an + n(n - 1)d ( subtract 2an from both sides )
2S - 2an = n(n - 1)d ← divide both sides by n(n - 1)
[tex]\frac{2S-2an}{n(n-1)}[/tex] = d
