9. Sequences, Series, & Induction

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence. Find a₇ when a₁ = 2, r = 3

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.${\sum }_{i=1}^6{\left(\frac{1}{2}\right)}^{i+1}$

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

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 a₅ when a₁ = -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, ...

Find the sum of each infinite geometric series. 3 + 3/4 + 3/4² + 3/4³ + ...

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

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.

${\sum }_{i=1}^6{5}^i$

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

Express each repeating decimal as a fraction in lowest terms. $0.\bar{5}=\frac{5}{10}+\frac{5}{100}+\frac{5}{1000}+\frac{5}{10,000}+\cdots$

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

Express each repeating decimal as a fraction in lowest terms. $0.\overline{47}=\frac{47}{100}+\frac{47}{10,000}+\frac{47}{1,000,000}+\cdots$

Find the sum of each infinite geometric series. -6 + 4 - 8/3 + 16/9 - ...