Find an explicit form f(n) for each of the following arithmetic sequences (assume a is some real number and x is
some real number).
b. 1 / 5, 1 / 10, 0, − 1 / 10,

The explicit form for this sequence is for all .

Step-by-step explanation:

The explicit form of an arithmetic sequence  of numbers   is given by the formula  , where    is the first term of the sequence,    is the difference between two consecutive terms of the sequence, and .

We know that  the first four elements for the arithmetic sequence are .

To find the general formula for this problem we only need to calculate in the above formula.

For n=2, we have

if we replace and and solve for we obtain  

Therefore the explicit form is   for all  .

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .