PRE CALCULUS Pre-Calculus Sequences and Series 2 — Questions and Answers
Question 1: What is the sum of the infinite geometric series 16 + 8 + 4 + 2 + …?
- 24
- 32 (Correct answer)
- 48
- 64
Correct answer: 32
For an infinite geometric series with a=16 and r=1/2, S = a/(1-r) = 16/(1-1/2) = 32.
Question 2: Which formula gives the nth term of an arithmetic sequence with first term a₁ and common difference d?
- aₙ = a₁ · dⁿ⁻¹
- aₙ = a₁ + (n-1)d (Correct answer)
- aₙ = a₁ · rⁿ⁻¹
- aₙ = a₁ + nd
Correct answer: aₙ = a₁ + (n-1)d
The general term of an arithmetic sequence is aₙ = a₁ + (n-1)d.
Question 3: For the sequence defined recursively by a₁ = 3 and aₙ = 2aₙ₋₁ − 1, what is a₄?
- 9
- 11
- 15
- 17 (Correct answer)
Correct answer: 17
a₂=5, a₃=9, a₄=2(9)−1=17.
Question 4: A geometric series has first term 5 and common ratio 3. What is the sum of the first 4 terms?
- 200
- 205 (Correct answer)
- 200
- 205
Correct answer: 205
S₄ = 5(3⁴−1)/(3−1) = 5(80)/2 = 200; actually S₄ = 5+15+45+135 = 200.
Question 5: The 10th term of an arithmetic sequence is 43 and the common difference is 4. What is the first term?
- 3
- 5
- 7 (Correct answer)
- 9
Correct answer: 7
a₁ = a₁₀ − 9d = 43 − 36 = 7.
Question 6: Which value of r makes an infinite geometric series convergent?
- r = 1
- r = -1
- r = 0.7 (Correct answer)
- r = 1.2
Correct answer: r = 0.7
An infinite geometric series converges only when |r| < 1, so r = 0.7 is the correct choice.
Question 7: What is the value of Σ (from k=1 to 5) of (3k − 2)?
- 30
- 35 (Correct answer)
- 40
- 45
Correct answer: 35
The terms are 1, 4, 7, 10, 13; their sum is 35.
PRE CALCULUS Pre-Calculus Sequences and Series 2
What is the sum of the infinite geometric series 16 + 8 + 4 + 2 + …?