Answer:
Step-by-step explanation:
Considering the geometric sequence


As the common ratio '
' between consecutive terms is constant.



The general term of a geometric sequence is given by the formula:

where
is the initial term and
the common ratio.
Putting
,
and
in the general term of a geometric sequence to determine the 12th term of the sequence.







∵ 

Therefore,
Answer:
So, solution of the differential equation is

Step-by-step explanation:
We have the given differential equation: y′′+4y=5xcos(2x)
We use the Method of Undetermined Coefficients.
We first solve the homogeneous differential equation y′′+4y=0.

It is a homogeneous solution:

Now, we finding a particular solution.

we get

So, solution of the differential equation is

It’s actually independent