Algebra Examples

Find the Sum of the Series 3+6+9+12
3+6+9+12
Step 1
This is the formula to find the sum of the first n terms of the sequence. To evaluate it, the values of the first and nth terms must be found.
Sn=n2(a1+an)
Step 2
This is an arithmetic sequence since there is a common difference between each term. In this case, adding 3 to the previous term in the sequence gives the next term. In other words, an=a1+d(n-1).
Arithmetic Sequence: d=3
Step 3
This is the formula of an arithmetic sequence.
an=a1+d(n-1)
Step 4
Substitute in the values of a1=3 and d=3.
an=3+3(n-1)
Step 5
Simplify each term.
Tap for more steps...
Step 5.1
Apply the distributive property.
an=3+3n+3-1
Step 5.2
Multiply 3 by -1.
an=3+3n-3
an=3+3n-3
Step 6
Combine the opposite terms in 3+3n-3.
Tap for more steps...
Step 6.1
Subtract 3 from 3.
an=3n+0
Step 6.2
Add 3n and 0.
an=3n
an=3n
Step 7
Substitute in the value of n to find the nth term.
a4=3(4)
Step 8
Multiply 3 by 4.
a4=12
Step 9
Replace the variables with the known values to find S4.
S4=42(3+12)
Step 10
Divide 4 by 2.
S4=2(3+12)
Step 11
Add 3 and 12.
S4=215
Step 12
Multiply 2 by 15.
S4=30
Step 13
Convert the fraction to a decimal.
S4=30
3+6+9+12
(
(
)
)
|
|
[
[
]
]
7
7
8
8
9
9
4
4
5
5
6
6
/
/
^
^
×
×
>
>
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
π
π
,
,
0
0
.
.
%
%
=
=
 [x2  12  π  xdx ]