Review Sequences and Series

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

What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47 + ...?

• 1,600
• 18,235
• 18,475
• 19,125

Find the 1st 6 terms of the sequence:
a_n = (n + 1)³

• 6, 9, 14, 21, 30, 41
• 3, 6, 9, 12, 15, 18
• 8, 27, 64, 125, 216, 343

Write the rule for the nth term:
2, 4, 6, 8, ...

• a_n = 2n
• a_n = n²
• a_n = (2)^n-1

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

You visit the Grand Canyon and drop a penny off the edge of a cliff.  The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence.  What is the total distance the object will fall in 6 seconds?
 

• 576 feet
• 144 feet
• 480 feet