9. Sequences, Series, & Induction

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

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a(sub 7) when a(sub 1) = 2, r = 3

In Exercises 31–36, find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 6 Σ (i = 1) (1/2)^(i + 1)

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a(sub 6) when a(sub 1) = 16, r = 1/2

In Exercises 37–44, find the sum of each infinite geometric series.1 + 1/3 + 1/9 + 1/27 + ...

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a(sub 5) when a(sub 1) = -3, r = 2

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a(sub n) to find a(sub 8), the eighth term of the sequence. 1, 2, 4, 8, ...

In Exercises 37–44, find the sum of each infinite geometric series.3 + 3/4 + 3/4^2 + 3/4^3 + ...

Find the sum of the first 15 terms of the geometric sequence: 5, -15, 45, -135

In Exercises 37–44, find the sum of each infinite geometric series.1 - 1/2 + 1/4 - 1/8 + ...

Use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum. *sigma notation* i=1 start, 6 end, 5^i formula

In Exercises 37–44, find the sum of each infinite geometric series.∞ Σ (i = 1) 8(- 0.3)^(i -- 1)

In Exercises 45–50, express each repeating decimal as a fraction in lowest terms.0.5 ̅ (repeating 5) = 5/10 + 5/100 + 5/1000 + 5/10,000 + ...