Can someone help me?

Question

solve for "a":

S= n/2 [2a+(n-1)d]

can someone show me the steps.

Answer 1

You want to isolate "a" on one side of the equation.

2S/n = 2a+(n-1)d
2a = 2S/n - (n-1)d
a = S/n - (n-1)d/2

Answer 2

Move the 2 and the n to the left hand side (LHS) of the equation, using multiplication and division:

2S/n = 2a + (n-1)d

Move the (n-1)d term to the LHS using subtraction:

2S/n - (n-1)d = 2a

Divide both sides by 2:

S/n - (n-1)d/2 = a

And you're done. You could rearange the LHS a bit if you want, but it doesn't really get any simpler.

Answer 3

Multiply by 2/n on both sides:

2S/n = 2a + (n-1)d

Subtract (n-1)d:

2S/n - (n-1)d = 2a

Divide by 2:

a = [2S/n - (n-1)d]/2 = S/n - (n-1)d/2.

Answer 4

S = n/2 [2a+(n-1)d] multiply by 2

2S = n[2a+(n-1)d] divide by n

(2S)/n = 2a+(n-1)d subtract [(n-1)d]

{[(2S)/n] - [(n-1)d]} = 2a divide by 2

{[(2S)/n] - [(n-1)d]}/2

Answer 5

1) Multiply both sides by 2:

2S = n[2a+(n-1)d]

2) Divde by n:

2S/N = 2a+(n-1)d

3) Move (n-1)d to left side

[(2S)/N] - (n-1)d = 2a

4) Divde by 2

Thus, a = [[2S/N] - (n-1)d]/2

Answer 6

remember back to PEMDAS?

well use those steps and u aint gonna go wrong

s = n/2 (2a + dn -d)
s * 2/n = 2a +dn - d
(2s/n) - dn + d = 2a
((2s/n) - dn + d)/2 = a


there u go, easy

Answer 7

S=n/2(2a +(n-1)d)
S= n/2(2a +nd -d)
= (2an/2 + (n/2)(nd) -nd/2
=an + nsquared(d)/2 -nd/2
S-nsq(d)/2 - nd/2 = an
1/n(S-nsq (d)/2 -nd/2) =a