Sequences and Series Quiz

Grade 10 · Math · Quiz

Test your knowledge of arithmetic and geometric sequences, nth terms, and series sums.

Questions

What is the 8th term of the arithmetic sequence 1, 4, 7, 10, ...?
1. 19
2. 22
3. 25
4. 28
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Answer: 22
a₁=1, d=3. a₈ = 1 + (8-1)·3 = 1 + 21 = 22.
The common ratio of the geometric sequence 5, 15, 45, 135, ... is ___.
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Answer: 3
r = 15/5 = 3. Each term is multiplied by 3.
What is the 5th term of the geometric sequence 2, 6, 18, ...?
1. 54
2. 108
3. 162
4. 486
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Answer: 162
a₁=2, r=3. a₅ = 2·3⁴ = 2·81 = 162.
The sequence 1, 1, 2, 3, 5, 8, 13, ... is an arithmetic sequence.
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Answer: False
This is the Fibonacci sequence — each term is the sum of the two preceding terms. Not arithmetic (no constant difference) and not geometric (no constant ratio).
The sum of the first 10 terms of the arithmetic series 2 + 5 + 8 + ... is:
1. 128
2. 145
3. 155
4. 170
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Answer: 145
a₁=2, d=3, n=10. a₁₀=2+(10-1)·3=29. Sₙ=n/2·(a₁+aₙ)=10/2·(2+29)=5·31=155.
For an arithmetic sequence, to find the nth term you use: aₙ = a₁ + (___)·d.
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Answer: n-1
aₙ = a₁ + (n-1)·d. We add d a total of (n-1) times to go from the 1st term to the nth term.
Which sequence is geometric?
1. 3, 7, 11, 15
2. 2, 4, 8, 16
3. 1, 3, 6, 10
4. 5, 10, 15, 20
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Answer: 2, 4, 8, 16
2,4,8,16: ratio = 2 (constant). The others are arithmetic (constant difference) or neither.
In a geometric sequence where r = 1, all terms are equal.
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Answer: True
If r=1, aₙ=a₁·1ⁿ⁻¹=a₁ for all n — every term equals the first term.
The sum of the arithmetic series 1 + 2 + 3 + ... + 100 equals:
1. 5000
2. 5050
3. 10100
4. 1000
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Answer: 5050
S₁₀₀ = 100/2·(1+100) = 50·101 = 5050. This is Gauss's famous result.
If a₁ = 3 and d = -2, then a₅ = ___.
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Answer: -5
a₅ = 3 + (5-1)·(-2) = 3 + 4·(-2) = 3 - 8 = -5.

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