Arithmetic Sequences
What type of sequence is this
5, 9, 13, 17,...
Arithmetic
What type of sequence is this:
6, 18, 54, 164,...
Geometric Sequence
What type of sequence is this
x_1=2
x_2=5
x_n=x_(x-1)+x_(x-2)
Neither
Write the generic recursive formula for arithmetic sequences:
3, 6, 9,...
a_1=3
a_n=a_(n-1)+3
What is the 10th term of the arithmetic sequence: 2, 6, 10, 14,...?
38
What is the 7th term of the geometric sequence: 3, 9, 27, 81,...?
2187
What is is the famous sequence in which each number is the sum of the two preceding ones. It is where the numbers and ratios in the sequence can be found in the patterns of petals of flowers, the whorls of a pine cone, and the leaves on stems. As the sequence continues, the ratios of the terms approach a number known as the golden ratio.
Fibonacci Sequence
Write the recursive formula for the geometric sequence:
6, 2, 2/3,...
g_1=6
g_n=g_(n-1)xx(1/3)
Find the common difference for this arithmetic sequence:
a_1=13
a_7=-11
Common Difference: 4
Find the sum of the first 7 terms of the geometric sequence: 5, 125, 525,...
97655
Find the 6th term of the sequence
x_1=2
x_2=5
x_n=x_(n-1)+x_(n-2)
31
Find the 6th term of this sequence:
g_1=999
g_n=g_(n-1)xx(1/3)
37/9
Find the sum of the first 15 terms of the arithmetic sequence: 4, 9, 14, 19
585
Find the common ratio for this geometric sequence:
a_1=4
a_4=864
Common Ratio: 6
Find the 4th term of the sequence
x_1=32
1/4(x_(n-1))+4
23/4
What is the sum of the first 40 terms
a_1=6
a_n=a_(n-1)+98
76680
How many terms are there in the arithmetic sequence: 20, 17, 14, ..., -13?
12 terms
How many terms are there in this geometric sequence: -9, 18, -36, ..., 1152.
8 terms
Find the sum of the first 9 terms of this sequence:
x_1=0, x_2=1
x_n=x_(n-1)+x_(n-2)
54
What is the sum of the first 11 terms for the recursive sequence:
g_1=3
g_n=g_(n-1)xx7
988,663,371
The Famous Hot Dog Eating Contest, in 2023, had 11 contestants where the first place winner received $100,000 while the last place person received $0. Every other person will receive a cash prize based on what place they finished in.
Write a recursive formula that represents the cash prize awarded in terms of the place in which the horse finishes (hint -> write common difference as a fraction, no decimals):
Write an explicit formula that represents the cash prize awarded in terms of the place in which each horse finishes (hint -> write common difference as a fraction, no decimals)
Compute the prize winnings for each place and round the cash value to the nearest hundredth place (use decimals):
Find the total amount of money distributed for this race:
1.
a_1=100000
a_n=a_(n-1)-10000
2.
a_n=110000-10000n
3. 1. $100,000, 2. $90,000, 3. $80,000, 4. $70,000, 5. $60,000, 6. $50,000, 7. $40,000, 8. $30,000, 9. $20,000, 10. $10,000, 11. $0
4. $550000