9. Sequences, Series, & Induction

In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r.Find a8 when a1 = 6, r = 2

In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r.Find a12 when a1 = 5, r = - 2

In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r.Find a40 when a1 = 1000, r = - 1/2

In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r.Find a8 when a1 = 1 000 000, r = 0.1

In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a7, the seventh term of the sequence.3, 12, 48, 192, ...

In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a7, the seventh term of the sequence.18, 6, 2, 2/3, ...

In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a7, the seventh term of the sequence.1.5, - 3, 6, -12, ...

In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a7, the seventh term of the sequence.0.0004, - 0.0004, 0.04, - 0.04, ...

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 12 terms of the geometric sequence: 2, 6, 18, 54, ...

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 11 terms of the geometric sequence: 3, - 6, 12, - 24, ...

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, ...

In Exercises 31–34, write the first five terms of each geometric sequence. a1 = 3, r = 2

In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 8 Σ (i = 1) 3^i

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

In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 10 Σ (i = 1) 5 · 2^i