An equation is said to have a constant of proportionality if 'x' is a multiple of 'y' or 'y' is a multiple of 'x'.
Now, we have to determine an equation with constant of proportionality as '1'.
1.
This equation has constant of proportionality as ''.
2.
This equation has constant of proportionality as ''.
3.
This equation has constant of proportionality as ''.
4.
This equation has constant of proportionality as '1'.
Option D is the correct answer.
Answer:
=
+ 3 ; a₁ = 1
Step-by-step explanation:
Given
1, 4, 7, 10, 13, 16, ......
Note the difference in consecutive terms is constant, that is
4 - 1 = 7 - 4 = 10 - 7 = 13 - 10 = 16 - 13 = 3
Thus to obtain the next term in the sequence ( recursive formula )
Add 3 to the previous term
=
+ 3 ( with a₁ = 1 )
To check for continuity at the edges of each piece, you need to consider the limit as approaches the edges. For example,
has two pieces, and
, both of which are continuous by themselves on the provided intervals. In order for
to be continuous everywhere, we need to have
By definition of , we have
, and the limits are
The limits match, so is continuous.
For the others: Each of the individual pieces of are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The filling in of the formula for the n-th term is pretty straightforward. The attachment shows how simple it is.
The 7th term is found by evaluating the expression for n=7.
a₇ = 192
