Arithmetic Sequences
What is the common difference of the sequence 18, 15, 12, 9, ...?
-3
What is the common ratio of the sequence:
f(1)=3, f(2)=6, f(3)=12, f(4)=24
2
S_n=n/2(a_1+a_2)
A fractal design has 1 triangle at stage 0, 4 at stage 1, and 16 at stage 2. How many triangles are at stage 3?
64
Classify the equation f(n)=5+3(n-1) as arithmetic or geometric
Arithmetic
Given f(1)=2 and f(n)=f(n-1)+4 for n>=2 what is f(4)?
14
Write a recursive definition for the sequence:
4, 12, 36, 108, ...
g(1)=4, g(n)=3*g(n-1), n>=2
Evaluate
\Sigma_(a=1)^5 (2a)
30
Is a paper-cutting pattern that repeatedly takes 1/3 of the remaining area arithmetic or geometric? Explain.
Geometric, because it involves repeated multiplication by a constant ratio
Classify the equation f(n)=5*3^(n-1) as arithmetic or geometric
geometric
Write an nth term rule where a(1)=62 and d=5
a(n)=62+5(n-1), n>=1
a(n)=5n+57, n>=0
Write an explicit rule for sequence f if
f(1)=3, f(n)2*f(n-1), n>=2
f(n)=3*2^(n-1), n>=1
Find the sum of the first 15 terms of an arithmetic sequence starting at 62 with a common difference of 5.
1,455
Write an explicit rule for the number of black squares at stage n if Stage 0 has 1 square, Stage 1 has 4, and Stage 2 has 16.
b(n)=4^n, n>=0
Convert the explicit rule: f(n)=3n+5, n>=0 into a recursive rule, specifying term 1, f(1)
f(1)=8, f(n)=f(n-1)+3, n>=2
Given a(1)=62 and a(n)=a(n-1)+5, n>=2 what is a(15) ?
132
A sheet of paper has an initial area of 81 cm^2 and each cut takes
1/3 of the previous. Write an explicit formula k(n) for the area after n cuts.
k(n)=81*(1/3)^n, n>=0
Evaluate \Sigma_(a=1)^20 (-2a+6)
-300
A growing block tower has 8 blocks in Step 1 and adds 3 blocks per step. Write an explicit equation f(n) for the number of blocks in step n .
f(n)=8+3(n-1), n>=1 or
f(n)=3n+5, n>=0
Explain the main difference between an explicit sequence equation and a recursive sequence equation.
An explicit formula calculates any term directly using its position n, while a recursive formula uses the previous term f(n-1) to find the next term.
Find the three missing terms in the arithmetic sequence.
14, ____, ____, ____, 38
20, 26, 32
If f(1)=64 and f(n)=1/2f(n-1) for n>=2 evaluate f(7)
1
Find the sum of all odd integers from 1 to 49, inclusive.
625
A student tracks total pages read after n days. From the set {-4, -0.5, 0, 0.25, 3, 5.8, 12}, which values are valid inputs for the domain of n?
0, 3, 12 (only non-negative whole numbers).
Convert the recursive rule f(1)=62, f(n)=f(n-1)+5, n>=2 into a simplified explicit equation in the form f(n)=mn+b
f(n)=5n+57