Sequences & Series Jeopardy Pythagora s Gauss Descart es Fibonacc i Fermat 100 200 300 400.
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Transcript of Sequences & Series Jeopardy Pythagora s Gauss Descart es Fibonacc i Fermat 100 200 300 400.
Sequences & Series Jeopardy
Pythagoras
GaussDescartes
Fibonacci
Fermat
100 100 100 100 100
200 200 200 200 200
300 300 300 300 300
400 400 400 400 400
100 Pythagoras
Find the 15th term in the following sequence:
-3, 3, 9,...81
200 Pythagoras
The 6th term of an arithmetic sequence is 46, and the difference is 3. What is the first term?
31
300 Pythagoras
Find the sum of the first 20 terms of the series
89 + 86 + 83 + ...
1210
400 Pythagoras
A geometric sequence has u6 = 24 and u11 = 768.
a) Find u17.
b) Find the sum of the first 15 terms.
49152
24575.25 ≈ 24600
100 Gauss
Find the next four terms of the sequence 343, 49, 7
1 1 11, , ,
7 49 343
200 Gauss
Find the 8th term for the sequence
3, -6, 12, ...
-384
300 Gauss
Find the formula for the general term un.3, 12, 21, 30, 39, …
un = 9n - 6
400 Gauss
A basketball is dropped vertically. It reaches a height of 2 meters on the first bounce. The height of each subsequent bounce is 90% of the previous bounce.a)What height does it reach on the 8th bounce?
b) What is the total vertical distance traveled by the ball between the 1st & 6th time the ball hits the ground?
0.957 meters
8.19 meters
100 Descartes
Find the sum of the first six terms of the series
2 + 3 + 4.5 + ….
665
16
200 Descartes
In an arithmetic series, u1 = -14 and u5 = 30
Find the sum of the first 5 terms.
40
300 Descartes
Find the general term un of the geometric sequence where u4 = 24 and u7 = 192
un = 3(2)n-1
400 Descartes
Find k given that 5, k, and k2 – 8 are consecutive terms of an arithmetic sequence. k = 3 or k = -1
100 Fibonacci
Find the 2004th term of the arithmetic series:-295, -290, -285, -280, -275, -270, …
9720
200 Fibonacci
The 6th term of an arithmetic sequence is 24. The common difference is 8.(a) Calculate the first term of the sequence.
(b) The sum of the first n terms is 600. Calculate the value of n.
-16
15
300 Fibonacci
Find the general term un of the geometric sequence where u3 = 8 and u6 = -1
11
322
n
nu
400 Fibonacci
Find k, given that k, k + 9, and 16k are consecutive terms of a geometric sequence.
9or 3
5k k
100 Fermat
Find the 8th term for the geometric sequence 3, -6, 12, ...
-384
200 Fermat
Write the formula for the general term un: 4, 7, 10, 13, …
un = 3n + 1
300 Fermat
Find the general term, un for an arithmetic sequence given that u7 = 72 and u15 = 112.
un = 5n + 37
400 Fermat
A woman deposits $100 into her son’s savings account on his first birthday. On his second birthday she deposits $125, $150 on his third birthday, and so on.(a) How much money would she deposit into her son’s account on his 17th birthday?
(b) How much in total would she have deposited after her son’s 17th birthday?
$500
$5100
Final Jeopardy
The sum of the first 7 terms of an arithmetic series is 329. The common difference is 14.Find the value of the first term.
u1 = 5