Find an expression for the nth term (tn) in each of the following sequence:
2 answers:
Answer:
===========================================
Work Shown:
The first term is a = 2 and the common difference is d = 4, since we're adding 4 to each term to get the next term.
Which is the answer.
--------------------------------
If you were to plug in say n = 3, then we get
showing that 10 is the third term, which matches with what the original sequence shows. I'll let you check the other values of n to fully confirm the answer.
You might be interested in
Answer:
Step-by-step explanation:
Component form of a vector is given by , where
represents change in x-value and
represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector
, the magnitude is
.
190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being , one leg being
, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.
In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
To find the other leg, , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:
Verify that
Therefore, the component form of this vector is