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Arithmetic & Geometric Sequences Quiz

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Arithmetic & Geometric Sequences Quiz

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Test basics of sequences.

Created by

Dennis Bico
Dennis Bico
Philippines

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Arithmetic & Geometric Sequences Quiz
 

Arithmetic & Geometric Sequences QuizOnline version

Test basics of sequences.

by Dennis Bico
1

1) Identify the sequence type and its common difference for 3, 7, 11, 15, ...

2

2) Identify the sequence type and common ratio for 2, 6, 18, 54, ...

3

3) Find nth term formula for arithmetic with a1 = 5 and d = 3.

4

4) Find nth term formula for geometric with a1 = 4 and r = 1/2.

5

5) Sum of first n terms of arithmetic with a1 = 2 and d = 5.

6

6) Sum of first n terms of geometric with a1 = 6 and r = 2.

7

7) Condition for convergence of an infinite geometric series.

8

8) If a_n = 7 + 4(n-1), find a_10.

9

9) Identify the sequence: 8, 4, 2, 1, ...

10

10) Which formula is the nth term for an arithmetic sequence?

Feedback

Arithmetic sequences have constant difference between terms; here 7-3=4.

Each term multiplies by the same factor 3.

For arithmetic, a_n = a1 + (n-1)d.

Geometric formula uses r^{n-1}.

Sum formula for arithmetic is S_n = n/2 [2a1 + (n-1)d].

Geometric sum S_n = a1(1 - r^n)/(1 - r).

Infinite geometric series converges only if |r| < 1.

Compute: 7 + 4(9) = 7 + 36 = 43.

Each term halves; geometric with r = 1/2.

Arithmetic nth term: a_n = a1 + (n-1)d.

 
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