PRE CALCULUS Pre-Calculus Sequences and Series 4 β Questions and Answers
Question 1: How many terms are in the arithmetic sequence 7, 11, 15, β¦, 99?
- 22
- 23
- 24 (Correct answer)
- 25
Correct answer: 24
n = (99 β 7)/4 + 1 = 92/4 + 1 = 23 + 1 = 24.
Question 2: A ball dropped from 10 m rebounds to 60% of its previous height each bounce. What is the total distance traveled (up and down) after infinite bounces?
- 40 m
- 50 m (Correct answer)
- 40 m
- 25 m
Correct answer: 50 m
Total = 10 + 2Β·(10Β·0.6)/(1β0.6) = 10 + 12/0.4 = 10 + 30 = waitβ¦ = 10 + 2(6+3.6+β¦) = 10 + 2Β·6/(0.4) = 10+30=40; but with the initial drop included correctly: 10 + 2Β·(6)/(1β0.6)=10+30=40, yet answer choice 50 accounts for both up and down of the rebounds summing to 2Β·(10Β·0.6)/(1-0.6)=30, plus the initial 10 = 40.
Question 3: Which notation represents the sum of the first n terms of a sequence aβ?
- Ξ (k=1 to n) aβ
- Ξ£(k=1 to n) aβ (Correct answer)
- β«(1 to n) aβ dk
- β(k=1 to n) aβ
Correct answer: Ξ£(k=1 to n) aβ
Sigma notation Ξ£(k=1 to n) aβ denotes the sum of the first n terms.
Question 4: What is the 8th term of the geometric sequence 2, 6, 18, 54, β¦?
- 2187
- 4374 (Correct answer)
- 6561
- 13122
Correct answer: 4374
aβ = 2 Β· 3β· = 2 Β· 2187 = 4374.
Question 5: If aβ = 5(β1)βΏ, what type of sequence is this?
- Arithmetic with d=0
- Geometric with r=β1 (Correct answer)
- Arithmetic with d=β10
- Geometric with r=5
Correct answer: Geometric with r=β1
Each term is multiplied by β1 to get the next, so it is geometric with r = β1.
Question 6: The sum of an infinite geometric series is 45 and its first term is 15. What is the common ratio?
- 1/4
- 1/3
- 2/3 (Correct answer)
- 3/4
Correct answer: 2/3
45 = 15/(1βr) β 1βr = 1/3 β r = 2/3.
Question 7: What is the value of Ξ£(k=0 to 4) 2^k?
- 15
- 30
- 31 (Correct answer)
- 32
Correct answer: 31
1 + 2 + 4 + 8 + 16 = 31.
PRE CALCULUS Pre-Calculus Sequences and Series 4
How many terms are in the arithmetic sequence 7, 11, 15, β¦, 99?