TMUA Sequences & Series 1 ā Questions and Answers
Question 1: The first term of an arithmetic sequence is 3 and the common difference is 5. What is the 10th term?
- 45
- 48 (Correct answer)
- 50
- 53
Correct answer: 48
The nth term of an arithmetic sequence is a + (n-1)d = 3 + 9Ć5 = 48.
Question 2: In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 5th term?
- 162 (Correct answer)
- 54
- 486
- 18
Correct answer: 162
The nth term of a geometric sequence is ar^(n-1) = 2 Ć 3^4 = 2 Ć 81 = 162.
Question 3: What is the sum of the first 20 terms of an arithmetic series with first term 4 and common difference 3?
- 620
- 650 (Correct answer)
- 680
- 700
Correct answer: 650
S_n = n/2 Ć (2a + (n-1)d) = 20/2 Ć (8 + 57) = 10 Ć 65 = 650.
Question 4: Which of the following sequences is arithmetic?
- 2, 4, 8, 16, ...
- 1, 3, 6, 10, ...
- 5, 8, 11, 14, ... (Correct answer)
- 1, 4, 9, 16, ...
Correct answer: 5, 8, 11, 14, ...
5, 8, 11, 14 has a constant common difference of 3, making it arithmetic.
Question 5: The nth term of a sequence is given by T_n = 2nĀ² ā n + 1. What is the value of T_4?
- 29 (Correct answer)
- 33
- 25
- 28
Correct answer: 29
T_4 = 2(4Ā²) ā 4 + 1 = 32 ā 4 + 1 = 29.
Question 6: A geometric series has first term 100 and common ratio 0.5. What is the sum to infinity?
- 150
- 200 (Correct answer)
- 250
- 100
Correct answer: 200
Sā = a/(1 ā r) = 100/(1 ā 0.5) = 100/0.5 = 200.
Question 7: In an arithmetic sequence, the 5th term is 17 and the 9th term is 33. What is the common difference?
- 2
- 3
- 4 (Correct answer)
- 5
Correct answer: 4
From a + 4d = 17 and a + 8d = 33, subtracting gives 4d = 16, so d = 4.
TMUA Sequences & Series 1
The first term of an arithmetic sequence is 3 and the common difference is 5.
What is the 10th term?