9. Sequences, Series, & Induction

Write a recursive formula for the geometric sequence $\(\left\]\lbrace\)18,6,2,\(\frac\)23,\(\ldots\[\right\]\rbrace\)$.

Exercises 88–90 will help you prepare for the material covered in the next section. Use the formula an = a₁3^(n-1) to find the seventh term of the sequence 11, 33, 99, 297,...

Let {a_n} = - 5, 10, - 20, 40, ..., {b_n} = 10, - 5, - 20, - 35, ..., {c_n} = - 2, 1, - 1/2, 1/4 Find a₁₀ + b₁₀.

Find the sum of each infinite geometric series. 1 + 1/3 + 1/9 + 1/27 + ...

Find the sum of each infinite geometric series. ${\sum }_{i=1}^{\infty }8(-0.3{)}^{i-1}$

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 14 terms of the geometric sequence: - 3/2, 3, - 6, 12, ...

Find a₂ and a₃ for each geometric sequence. 8, a₂, a₃, 27

Write the first five terms of each geometric sequence. a₁ = 20, r = 1/2

Let {a_n} = - 5, 10, - 20, 40, ..., {b_n} = 10, - 5, - 20, - 35, ..., {c_n} = - 2, 1, - 1/2, 1/4 Find the difference between the sum of the first 10 terms of {a_n} and the sum of the first 10 terms of {b_n}.

Find the sum of each infinite geometric series. 1 - 1/2 + 1/4 - 1/8 + ...

In Exercises 31–34, write the first five terms of each geometric sequence. a1 = 1/2, r = 1/2