9. Sequences, Series, & Induction

In Exercises 45–50, express each repeating decimal as a fraction in lowest terms.0.257 ̅ (repeating 257)

Express each repeating decimal as a fraction in lowest terms. 0.6 (repeating 6)

In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = n + 5

In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = 2^n

In Exercises 51–56, the general term of a sequence is given. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.an = n^2 + 5

In Exercises 57–62, let{a_n} = - 5, 10, - 20, 40, ..., {b_n} = 10, - 5, - 20, - 35, ...,{c_n} = - 2, 1, - 1/2, 1/4Find a10 + b10.

In Exercises 57–62, let{a_n} = - 5, 10, - 20, 40, ..., {b_n} = 10, - 5, - 20, - 35, ...,{c_n} = - 2, 1, - 1/2, 1/4Find the difference between the sum of the first 10 terms of {an} and the sum of the first 10 terms of {bn}.

In Exercises 63–64, find a2 and a3 for each geometric sequence.8, a2, a3, 27

In Exercises 63–64, find a2 and a3 for each geometric sequence.2, a2, a3, - 54

Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence 1, −2, 4, −8, 16, ………. Find a2/a3, a1/a2, a4/a3 and a5/a4 What do you observe?

Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence whose nth term is an = (3)5^n Find a2/a3, a1/a2, a4/a3 and a5/a4 What do you observe?

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,...