Answer:
See explanation
Step-by-step explanation:
The given circle has center O.
A, B,C, and D are points on the circumference of the circle.
We want to prove that:
We need to join to B and C as shown in the attachment.
Recall that angle subtended by arc BC at the center is twice the angle subtended at the circumference by the same arc.
This implies that:
The LHS of equation (1) and (2) are equal. Therefore the RHS are also equal.
This implies that:
Answer:
Step-by-step explanation:
The equation for an arithmetic sequence is
where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.
Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:
which simplifies to
and a bit more to
(which should tell you that arithmetic sequences are lines!)
Finding the 13th number simply requires that we replace n with 13 and solve:
so