How to Solve Problems in Arithmetic Series Using Formulas?

[bananaman13]

I don't understand on how to get the answer of a certain problem in arithmetic series.

formula/s:

Arithmetic means
An=A1+ (n-1)d

Arithmetic series
Sn=n/2 (A1+An)

I understand on how to get the terms to these but when finding for:

Find A1 if,
S10= -20 , d= 4

&

Find S12 if, 2+5+8+...

I couldn't quite grasp the idea on how to apply the formulas to these problems.

Any help is appreciated. Thank you very much

 

[smart_worker]

Sn=n/2 (A1+An)

this can also be written as Sn=n/2 (A1+(A1+ (n-1)d))

which then further simplifies to: Sn=n/2 (2A1+ (n-1)d)

now plug in the known values and simplify

for your first question, the value of n=10

for your second question,
n=12,d=3,A1=2

 

[bananaman13]

Thank you so much.

So, in which case,

Sn=n/2 (A1+An) is still equal to
Sn=n/2 [2A1+(n-1)d]

Just different in how to solve it.