Answer:
The required formula is:
Step-by-step explanation:
The total number of squares of the the first term = 4
The total number of squares of the the second term = 7
The total number of squares of the the third term = 10
so,
Finding the common difference d
As the common difference 'd' is same, it means the sequence is in arithmetic.
So
If the initial term of an arithmetic progression is 
and the common difference of successive members is d, then the nth term of the sequence 
is given by:
Therefore, the required formula is:
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Correct me if im wrong but the answer is (B) hope this helps!
Answer:
2.c 3.a 4.b
Step-by-step explanation:
just looked at it carefully
Take the homogeneous part and find the roots to the characteristic equation:
This means the characteristic solution is
.
Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form
. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.
With
and
, you're looking for a particular solution of the form
. The functions
satisfy
where
is the Wronskian determinant of the two characteristic solutions.
So you have
So you end up with a solution
but since
is already accounted for in the characteristic solution, the particular solution is then
so that the general solution is
