ECAT — Engineering College Admission Test (UET)

ECAT Mathematics — Sequences and Series (Set 1)

Take the ECAT Mathematics — Sequences and Series (Set 1): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer review. Covers…

What this test covers

30 ECAT Mathematics

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

Q1. The 20th term of the arithmetic progression 3, 7, 11, 15, … is:
- A. 83
- B. 80
- C. 79 ✓
- D. 75
Answer: C. 79
Explanation: a₂₀ = a + 19d = 3 + 19 × 4 = 79.
Q2. Which term of the A.P. 5, 8, 11, … is 59?
- A. 20th
- B. 19th ✓
- C. 18th
- D. 17th
Answer: B. 19th
Explanation: 5 + (n − 1)3 = 59 ⇒ n − 1 = 18 ⇒ n = 19.
Q3. The arithmetic mean between 7 and 19 is:
- A. 13 ✓
- B. 26
- C. 12
- D. √133
Answer: A. 13
Explanation: A.M. = (7 + 19)/2 = 13.
Q4. The three arithmetic means inserted between 2 and 18 are:
- A. 6, 12, 18
- B. 6, 10, 14 ✓
- C. 4, 8, 12
- D. 5, 10, 15
Answer: B. 6, 10, 14
Explanation: With 5 terms in all, 18 = 2 + 4d ⇒ d = 4, giving 6, 10, 14.
Q5. The sum of the first 15 terms of the series 2 + 5 + 8 + … is:
- A. 360
- B. 330
- C. 690
- D. 345 ✓
Answer: D. 345
Explanation: S₁₅ = (15/2)[2(2) + 14(3)] = (15/2)(46) = 345.

The other 25 questions

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Q6. The sum of the first n odd natural numbers 1 + 3 + 5 + … is:
- A. n²
- B. n(n + 1)
- C. 2n − 1
- D. n(n + 1)/2
Q7. The 8th term of the geometric progression 3, 6, 12, … is:
- A. 768
- B. 48
- C. 384
- D. 192
Q8. The positive geometric mean between 4 and 25 is:
- A. 10
- B. 5
- C. 14.5
- D. 100
Q9. The sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + … is:
- A. 2
- B. 3/2
- C. 3
- D. 4/3
Q10. Expressed as a sum of an infinite G.P., the recurring decimal 0.777… equals:
- A. 7/10
- B. 77/100
- C. 7/99
- D. 7/9
Q11. An infinite geometric series a + ar + ar² + … has a finite sum if and only if:
- A. r = 1
- B. |r| < 1
- C. r > 1
- D. |r| > 1
Q12. The sum of the first 6 terms of the G.P. 2, 4, 8, … is:
- A. 126
- B. 128
- C. 254
- D. 64
Q13. The harmonic mean between 4 and 12 is:
- A. 6
- B. √48
- C. 8
- D. 16/3
Q14. For two positive numbers, the arithmetic mean is 10 and the harmonic mean is 6.4. Their geometric mean is:
- A. 64
- B. 8.2
- C. 6.8
- D. 8
Q15. The 10th term of the harmonic progression 1/2, 1/5, 1/8, … is:
- A. 1/32
- B. 1/29
- C. 1/27
- D. 29
Q16. The value of 1² + 2² + 3² + … + 10² is:
- A. 3025
- B. 505
- C. 55
- D. 385
Q17. The value of 1³ + 2³ + 3³ + 4³ + 5³ is:
- A. 15
- B. 225
- C. 125
- D. 275
Q18. The sum 1·2 + 2·3 + 3·4 + … + 10·11 is:
- A. 495
- B. 330
- C. 385
- D. 440
Q19. If x + 1, 3x and 4x + 2 are consecutive terms of an A.P., then x equals:
- A. 1
- B. −3
- C. 3
- D. 2
Q20. Three numbers in A.P. have sum 15 and product 80. The largest of them is:
- A. 10
- B. 8
- C. 6
- D. 7
Q21. If k, 2k + 2 and 3k + 3 are consecutive terms of a G.P. (with k ≠ −1), then k equals:
- A. −4
- B. 2
- C. 4
- D. −1/4
Q22. If the sum of the first n terms of a sequence is Sₙ = 3n² + 2n, then its 5th term is:
- A. 33
- B. 85
- C. 29
- D. 17
Q23. The sum of the infinite series 1 + 2(1/2) + 3(1/2)² + 4(1/2)³ + … is:
- A. 2
- B. 8
- C. 4
- D. 3
Q24. In an A.P., the 3rd term is 10 and the 7th term is 22. The common difference is:
- A. 3
- B. 4
- C. 12
- D. 2
Q25. The 2nd term of a G.P. is 6 and its 5th term is 48. The first term is:
- A. 2
- B. 6
- C. 1.5
- D. 3
Q26. How many terms are there in the A.P. 7, 11, 15, …, 99?
- A. 24
- B. 22
- C. 23
- D. 25
Q27. An infinite G.P. has first term 4 and sum 12. Its common ratio is:
- A. −2/3
- B. 1/3
- C. 3/4
- D. 2/3
Q28. The 5th term of the sequence defined by aₙ = (−1)ⁿ(2n + 1) is:
- A. 9
- B. −11
- C. −9
- D. 11
Q29. A sequence is defined by a₁ = 2 and aₙ₊₁ = 3aₙ − 1. The value of a₄ is:
- A. 122
- B. 14
- C. 41
- D. 40
Q30. The sum of all integers from 1 to 100 that are divisible by 5 is:
- A. 1050
- B. 2100
- C. 1100
- D. 1000