91Ó°ÊÓ

Write the repeating decimal as a fraction in simplest form. \(130.130130130 \ldots\)

Find two infinite geometric series whose sums are each 6 . Justify your answers.

In Exercises 23-30, write a rule for the \(n\)th term. Then graph the first six terms of the sequence. $$ a_2=30, r=\frac{1}{2} $$

Describe the pattern, write the next term, and write a rule for the \(\boldsymbol{n}\) th term of the sequence. \(1.2,4.2,9.2,16.2, \ldots\)

write a rule for the nth term of the sequence. Then graph the fi rst six terms of the sequence. \(a_{21}=-25, d=-\frac{3}{2}\)

The Sierpinski triangle is a fractal created using equilateral triangles. The process involves removing smaller triangles from larger triangles by joining the midpoints of the sides of the larger triangles as shown. Assume that the initial triangle has an area of 1 square foot. a. Let \(a_n\) be the total area of all the triangles that are removed at Stage \(n\). Write a rule for \(a_n\). b. Find \(\sum_{n=1}^{\infty} a_n\). Interpret your answer in the context of this situation.

write a rule for the nth term of the arithmetic sequence. \(a_6=-8, a_{15}=-62\)

Write a recursive rule for the sequence. $$ a_n=12(11)^{n-1} $$

write a rule for the nth term of the arithmetic sequence. \(a_8=-15, a_{17}=-78\)

In Exercises 33-40, write a rule for the \(n\)th term of the geometric sequence. $$ a_1=1, a_2=49 $$