7.1 Sequences and series practice 1

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Question 1 of 6

1. Question

Write the first 5 terms of each sequence.

(a) [math]a_1=3, a_n=a_{n-1}+2n[/math]

(b) [math]b_n=(-1)^n(n-1)[/math]

(c) [math]C_0=0, C_1=1, C_{2n}=C_n, C_{2n+1}=C_n+C_{n-1}[/math]

(a) [math]=[/math] BLANK 1 of 15 , BLANK 2 of 15 , BLANK 3 of 15 , BLANK 4 of 15 , BLANK 5 of 15 (b) [math]=[/math] BLANK 6 of 15 , BLANK 7 of 15 , BLANK 8 of 15 , BLANK 9 of 15 , BLANK 10 of 15 (c) [math]=[/math] BLANK 11 of 15 , BLANK 12 of 15 , BLANK 13 of 15 , BLANK 14 of 15 , BLANK 15 of 15
(a) [math]=[/math] Fill in the blank 1 of 15 , Fill in the blank 2 of 15 , Fill in the blank 3 of 15 , Fill in the blank 4 of 15 , Fill in the blank 5 of 15

(b) [math]=[/math] Fill in the blank 6 of 15 , Fill in the blank 7 of 15 , Fill in the blank 8 of 15 , Fill in the blank 9 of 15 , Fill in the blank 10 of 15

(c) [math]=[/math] Fill in the blank 11 of 15 , Fill in the blank 12 of 15 , Fill in the blank 13 of 15 , Fill in the blank 14 of 15 , Fill in the blank 15 of 15

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Question 2 of 6

2. Question

Find the [math]n^{th}[/math] term of the series with [math]S_n=\dfrac{1}{4}n^2(n+1)^2[/math]

BLANK 1 of 4[math]n^3+[/math]BLANK 2 of 4[math]n^2+[/math]BLANK 3 of 4[math]n+[/math]BLANK 4 of 4
Fill in the blank 1 of 4 [math]n^3+[/math]Fill in the blank 2 of 4 [math]n^2+[/math]Fill in the blank 3 of 4 [math]n+[/math]Fill in the blank 4 of 4

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Question 3 of 6

3. Question

(Calculator) Let [math]p_1=3[/math], and [math]p_{k+1}=4p_k+5[/math] for all integers [math]k\geq1[/math]. What is [math]p_6[/math]?

BLANK 1 of 1
Fill in the blank 1 of 1

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Question 4 of 6

4. Question

Find the [math]2000^{th}[/math] term of this sequence [math]a_n=(a_{n-1}-a_{n-2})+2[/math] when [math]a_1=5, a_2=7[/math]. (hint: look for the pattern, and you need some patience)

BLANK 1 of 1
Fill in the blank 1 of 1

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Question 5 of 6

5. Question

[math]1[/math]

[math]2[/math]

[math]3[/math]

[math]4[/math]

[math]5[/math]

[math]6[/math]

[math]7[/math]

[math]8[/math]

[math]9[/math]

[math]10[/math]

[math]11[/math]

[math]12[/math]

[math]f_n[/math]

[math]1[/math]

[math](f_{n+2})^2-(f_n)^2[/math]

(a)

(b)

(c)

(d)

(e)

Let [math]f_n[/math] be the [math]n^{th}[/math] Fibonacci number.(a)

(a)-(e) Complete the table

(f) [math](f_{n+2})^2-(f_n)^2 =[/math]
(A) [math]f_{2n+2}[/math]
(B) [math]f_{2n}[/math]
(C) [math]f_{2n-2}[/math]
(D) [math]f^2_{2n}[/math]

(a) BLANK 1 of 6 (b) BLANK 2 of 6 (c) BLANK 3 of 6 (d) BLANK 4 of 6 (e) BLANK 5 of 6 (f) BLANK 6 of 6

(a) Fill in the blank 1 of 6

(b) Fill in the blank 2 of 6

(d) Fill in the blank 4 of 6

(e) Fill in the blank 5 of 6

(f) Fill in the blank 6 of 6

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Question 6 of 6

6. Question

The sequence below is defined using recursion formula:[math]a_1=3, a_2=0.8[/math], and [math]a_n=2a_{n-2}+5a_{n-1}-11[/math]

[math]a_3=[/math]BLANK 1 of 2 [math]a_4=[/math]BLANK 2 of 2
[math]a_3=[/math]Fill in the blank 1 of 2

[math]a_4=[/math]Fill in the blank 2 of 2

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7.1 Sequences and series practice 1

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