Sequences and Series Review

Arithmetic Sequences

100

The common difference of the sequence -34, -64, -94, -124...

What is d=-30

200

The first 4 terms of the sequence: a_n=15+6(n-1)

What is: a₁= 15, a₂=21, a₃=27, a₄=33

300

The 34^th term of the sequence defined as a_n=-11+7n

What is 227?

400

The explicit formula (in linear form) of the sequence with a₃₇=249 and d = -8 

What is a_n = 545 - 8n ?

500

The explicit formula (in linear form) of the arithmetic sequence with 44.3 as the 18^th term and 84.8 as the 33^rd term.

What is a_n = 2.7n - 4.3?

Arithmetic Series

100

What is the sum of the first 35 terms of a sequence with explicit formula 

a_n = 5n - 2?

What is 3080?

200

The sum of the first 45 terms of a sequence with the explicit formula a_n=3n-9

What is 2700?

300

The sum when n=15 of the series 20 + 30 + 40 +...

What is 1350?

400

The sum from n=1 to 141 with the explicit formula (-2n + 1)

What is -19,881?

500

The sum of this series: 14 + 17 + 20 +...+ 116

What is 2275?

Geometric Sequences

100

The common ratio of 4, 16, 36, 64... if the sequence is geometric

What is not a geometric sequence?

200

The first four terms of the sequence with explicit formula a_n = -4*3^n-1

What is: a₁=-4, a₂=-12, a₃=-36, a₄=-108

300

The first four terms and the explicit formula of a sequence where a₁=-3 and r=-3

What is: a₁=-3, a₂=9, a₃=-27, a₄=81 and a_n=-3(-3)^n-1

400

The missing terms of the geometric sequence: 

-729, ____, _____, _____, -144

What is -486, -324, -216 ?

500

The 8^th term and 1^st term of a sequence with a₅ = 768 and a₂ = 12

What is a₈ = 49,152 and a₁ = 3?

Geometric Series

100

The sum of the first 9 terms of the sequence a_n=4(3)^n-1

What is 39,364?

200

The sum of the infinite geometric series where a₁=1 and r=-4

What is no sum?

300

The sum of the finite series: (-5) + (-15) + (-45) +...; n=11

What is -442,865?

400

The sum of the infinite series: 4 + 2 + 1 + 1/2 +... 

What is 8?

500

The number of terms (n) in a finite geometric series if a₁= -3, r=4, and S_n=-4095

What is 6?

Miscellaneous

100

What is Blu's main problem in the beginning of Rio?

What is he can't fly?

200

What is the date today?

What is June 8^th, 2021?

300

The sequence is either arithmetic, geometric, or neither. If possible, state the common difference or common ratio.

1/2, 1, 2, 4,...

What is geometric and r=2

400

What comes down but never goes up?

What is rain?

500

The next three terms of the sequence 0, 3, 8, 15, 24,...

What is 35, 48, 63?