Arithmetic & Geometric Sequences Quiz

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Test basics of sequences.

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Dennis Bico

Philippines

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Arithmetic & Geometric Sequences Quiz


Arithmetic & Geometric Sequences QuizVersion en ligne Test basics of sequences. par Dennis Bico 1 1) Identify the sequence type and its common difference for 3, 7, 11, 15, ... a Arithmetic, d = 4 b Geometric, r = 4/ c Geometric, r = 4 d Arithmetic, d = -4 2 2) Identify the sequence type and common ratio for 2, 6, 18, 54, ... a Arithmetic, d = 1 b Geometric, r = 2 c Geometric, r = 3 d Arithmetic, d = 3 3 3) Find nth term formula for arithmetic with a1 = 5 and d = 3. a a_n = 5 + (n+1)3 b a_n = 5 - (n-1)3 c a_n = 5 + n/3 d a_n = 5 + (n-1)3 4 4) Find nth term formula for geometric with a1 = 4 and r = 1/2. a a_n = 4(2)^{n-1} b a_n = 4 + (1/2)^{n-1} c a_n = 4/(1/2)^{n-1} d a_n = 4(1/2)^{n-1} 5 5) Sum of first n terms of arithmetic with a1 = 2 and d = 5. a S_n = n/2[2 + (n-1)5] b S_n = n/2[22 + (n-1)5] c S_n = n[22 + (n-1)5] d S_n = n/2[2*2 - (n-1)5] 6 6) Sum of first n terms of geometric with a1 = 6 and r = 2. a S_n = 6(1-2^n) b S_n = 6n(1-2) c S_n = 6(1-2^n)/(1-2) = 6(2^n - 1) d S_n = 6(1+2^n)/(1+2) 7 7) Condition for convergence of an infinite geometric series. a \|r\| < 1 b r = 0 c \|r\| = 1 d \|r\| > 1 8 8) If a_n = 7 + 4(n-1), find a_10. a a_10 = 49 b a_10 = 47 c a_10 = 43 d a_10 = 37 9 9) Identify the sequence: 8, 4, 2, 1, ... a Geometric, a1 = 8, r = 2 b Arithmetic, d = -1 c Geometric, a1 = 8, r = 1/2 d Arithmetic, d = -4 10 10) Which formula is the nth term for an arithmetic sequence? a a_n = a1 + nd b a_n = a1 + (n-1)d c a_n = a1 - (n-1)d d a_n = a1 r^{n-1} Feedback 1 Arithmetic sequences have constant difference between terms; here 7-3=4. 2 Each term multiplies by the same factor 3. 3 For arithmetic, a_n = a1 + (n-1)d. 4 Geometric formula uses r^{n-1}. 5 Sum formula for arithmetic is S_n = n/2 [2a1 + (n-1)d]. 6 Geometric sum S_n = a1(1 - r^n)/(1 - r). 7 Infinite geometric series converges only if \|r\| < 1. 8 Compute: 7 + 4(9) = 7 + 36 = 43. 9 Each term halves; geometric with r = 1/2. 10 Arithmetic nth term: a_n = a1 + (n-1)d.

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Arithmetic & Geometric Sequences Quiz

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À propos de cette activité

Créé par

Téléchargez la version pour jouer sur papier

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Arithmetic & Geometric Sequences QuizVersion en ligne

par Dennis Bico

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

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

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

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

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

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

7) Condition for convergence of an infinite geometric series.

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

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

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

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