Arithmetic and Geometric Sequences

Question 1

What is the general form for an arithmetic sequence?

Answer 1

a1, a1 + d, a1 + 2d, a1 + 3d, - - - -

Question 2

What is the formula for the nᵗʰ term in an arithmetic sequence, aₙ?

Answer 2

aₙ = a1 + (n - 1) * d

Question 3

What is the formula for the sum of the first n terms of an arithmetic sequence, Sₙ?

Answer 3

Sₙ = n(a1 + aₙ)/2

Question 4

What is the general form for a geometric sequence?

Answer 4

a, ar, ar², . . . , ar⁽ⁿ ⁻ ¹⁾

Question 5

What is the formula for the sum of the first n terms of a geometric sequence, Sₙ?

Answer 5

n - 1 Σ k = 0 (arᵏ) = a (1 - rⁿ/1 - r)

Question 6

In a geometric sequence, what happens when n goes to infinity and r is less than 1 but greater than -1?

Answer 6

rⁿ approaches zero, and we ∞ ∑ k = 0 (arᵏ) = a(1/1 - r)