Geometric Series Formula

Which of the following is DIVERGENT?

• 10+6+2+-2+...
• 25+5+1+0.2+...
• 100+50+25+5+...
• 3(.25)ⁿ = A_n

Find the infinite sum of the series A_n = 2(1/3)ⁿ

• S = 2
• S = 1
• S = 3
• S is not finite

What does the formula S = A₁/(1-r) give you?

• The finite sum of an arithmetic series.
• The infinite sum of a geometric series.
• The partial sum of a geometric series.
• The infinite sum of an arithmetic series.

What does S_n = (n/2)(A₁ + A_n) give you?

• The nth partial sum of a geometric series.
• The nth partial sum of any series.
• The nth partial sum of an arithmetic series.
• The infinite sum of absolutely any series in the whole wide world.

Find the common ratio: 16, 8, 4, 2, ...

• r = 2
• r = 8
• r = 1/4
• r = 1/2

Find the common ratio: -3, -9, -27, -81, ...

• r = 6
• r = -6
• r = 3
• r = -3

Determine the sum of the series written in Sigma Notation. 

• -65104
• -71570
• -73483
• -22003

Determine the sum of the series written in Sigma Notation. 

• -341
• -279
• -250
• -431

Find the rule for this geometric sequence:
r = 3            a₃ = -12   

• a_n = (-4/3) (3)^n-1
• a_n = -4 (3)^n-1
• a_n = (-3/4) (3) ^n-1

Calculate the sum of the terms of the following geometric sequence:
1, 1/2, 1/4, 1/8, 1/16...

• 2
• 3
• 1