9. Sequences, Series, & Induction

Write the first five terms of each geometric sequence. a₁ = 5, r = 3

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 6 terms of {a_n} and the sum of the infinite seris containing all the terms of {c_n}.

Write the first five terms of each geometric sequence. a₁ = 3, r = 2

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.${\sum }_{i=1}^8{3}^i$

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

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. ${\sum }_{i=1}^{10}5\cdot 2^i$

Use the formula for the sum of the first n terms of a geometric sequence to find the indicated sum.

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

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, ...

Write a formula for the general or $n^{\(\th\)}$ term of the geometric sequence where $a_7=1458$ and $r=-3$.

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

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