Answer:
[tex]n=\frac{4as -2ds}{(1-2ds)}[/tex]
Step-by-step explanation:
[tex]S= \frac{n}{2 [2a + (n - 1)d]}[/tex]
Simplifying the fraction by multiplying d into the (n-1) term,
[tex]s=\frac{n}{2 [2a + (n - 1)d] } = \frac{n}{2[2a + dn - d] }[/tex]
Simplifying the fraction by multiplying 2 throughout,
[tex]s= \frac{n}{4a + 2dn-2d}[/tex]
Multiply [tex](4a + 2dn-2d)[/tex] on both sides
[tex](4a + 2dn-2d)s= \frac{n}{4a + 2dn-2d} (4a + 2dn-2d)[/tex]
Cancel the [tex](4a + 2dn-2d)[/tex] on the right hand side
[tex](4a + 2dn-2d)s= n[/tex]
Multiply s to the terms,
[tex]4as + 2dns-2ds= n[/tex]
Move [tex]2dns[/tex] to the right hand side by subtracting [tex]2dns[/tex] on both sides[tex]4as + 2dns-2ds-2dns= n-2dns[/tex]
[tex]4as -2ds= n-2dns[/tex]
On the right hand side of the equation, take out [tex]n[/tex]
[tex]4as -2ds= n(1-2ds)[/tex]
Divide Left hand side by [tex](1-2ds)[/tex],
[tex]n=\frac{4as -2ds}{(1-2ds)}[/tex]
