Answer:
Step-by-step explanation:
Let
denote the <em>k</em>th term of the sequence. Then

where <em>d</em> is the common difference between consecutive terms in the sequence and <em>a</em>₁ is the first term.
The sum of the first <em>n</em> terms is

From the formula for
, we get




So we have
, and
so that
.
Then the <em>n</em>th term in the sequence is

Answer:
It will always be the case when A and B are opposites
Step-by-step explanation:
sin(x) = -sin(-x) so ...
sin(A -A) = (A -A) = sin(A) -sin(A) = 0
That is, the given expression is true when B=-A.
Arc PR is 156 degrees. Since both angles are are making the forming arc they should be congruent. You can put (5x+23)=(9x-21) which is x=11.
Then you plug in 11 into your equation; 5(11)+23=78.
Since the vertex is on the outside of the circle then the arc is forms is 2 times the value of the angle.
78(2)=156