19. Sequences and Series

Question 1

Sequence

Series

Answer 1

An ordered list of numbers.

Sum of the terms of a sequence.

Question 2

Arithmetic sequence vs. Geometric sequence

Answer 2

Arithmetic: constant difference between successive terms.

Geometric: constant ratio between successive terms.

Question 3

nth term of an arthmetic sequence

Answer 3

t_n = t₁ + (n – 1)d

Question 4

Sum of n terms of an arithmetic sequence

(Arithmetic Series)

Answer 4

S_n = n/2 (t₁ + t_n)

Question 5

nth term of a geometric sequence

Answer 5

t_n = t₁•r^n–1

Question 6

Sum of n terms of a geometric sequence

(Geometric Series)

Answer 6

S_n = t₁ (1 – rⁿ) / (1 – r)

Question 7

If |r| < 1, S_∞ =

(Convergence)

Answer 7

lim_{<em>n</em>→∞}S_n =

S = t₁ / (1 – r)