ECAT — Engineering College Admission Test (UET)
Take the ECAT Mathematics — Sequences and Series (Set 3): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer review. Covers…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. The sum of the first n terms of a sequence is Sₙ = 3n² + 2n. Its 10th term is:
Answer: D. 59
Explanation: a₁₀ = S₁₀ − S₉ = 320 − 261 = 59.
Q2. In an A.P., the 3rd term is 10 and the 7th term is 22. The 10th term is:
Answer: C. 31
Explanation: 4d = 12 ⇒ d = 3 and a = 4. a₁₀ = 4 + 9 × 3 = 31.
Q3. The sum of all multiples of 9 lying between 10 and 200 is:
Answer: A. 2268
Explanation: The multiples are 18, 27, …, 198: 21 terms. Sum = 21/2 × (18 + 198) = 2268.
Q4. The sum of the series 100 + 96 + 92 + … + 4 is:
Answer: D. 1300
Explanation: Number of terms: (100 − 4)/4 + 1 = 25. Sum = 25/2 × (100 + 4) = 1300.
Q5. Four arithmetic means are inserted between 3 and 23. Their sum is:
Answer: C. 52
Explanation: With d = (23 − 3)/5 = 4 the means are 7, 11, 15, 19, whose sum is 52 (= 4 × the average of 3 and 23 = 4 × 13).
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Q6. The sum of the first six terms of the G.P. 2, 6, 18, … is:
Q7. In a G.P. of positive terms the 2nd term is 6 and the 5th term is 162. The 4th term is:
Q8. An infinite G.P. has first term 10 and sum 25. Its common ratio is:
Q9. The sum to infinity of 1 − 1/3 + 1/9 − 1/27 + … is:
Q10. The sum to infinity of the G.P. 8, −4, 2, −1, … is:
Q11. The sum to infinity of a G.P. is 6 and its common ratio is 2/3. The first term is:
Q12. Two geometric means are inserted between 3 and 81. Their product is:
Q13. The A.M. and G.M. of two positive numbers are 10 and 8. Their H.M. is:
Q14. In a harmonic progression the 4th term is 1/10 and the 7th term is 1/16. The 10th term is:
Q15. The sum 1² + 3² + 5² + 7² + 9² is:
Q16. The sum 1·3 + 2·4 + 3·5 + … + 10·12 is:
Q17. The sum to infinity of 1/2 + 2/4 + 3/8 + 4/16 + … is:
Q18. A sequence is defined by a₁ = 2 and aₙ₊₁ = 3aₙ − 1. The fifth term a₅ is:
Q19. Three numbers in A.P. have sum 21 and product 315. The greatest of them is:
Q20. Three positive numbers in G.P. have sum 14 and product 64. The middle number is:
Q21. If a, b, c are in A.P., then 2ᵃ, 2ᵇ, 2ᶜ are in:
Q22. If x, 4, 3 are in harmonic progression, then x equals:
Q23. The smallest positive integer n for which 1 + 2 + 3 + … + n exceeds 500 is:
Q24. The sum 1 + 3 + 9 + … + 3⁹ equals:
Q25. The sum of 1/(1·2) + 1/(2·3) + … + 1/(19·20) is:
Q26. A person's salary is Rs 30,000 in the first year and rises by Rs 2,000 every year. The total earned in the first 10 years is:
Q27. A ball is dropped from 16 m and after each fall rebounds to 3/4 of the previous height. The total distance it travels before coming to rest is:
Q28. In an A.P. the sum of the first 10 terms equals the sum of the first 20 terms. The sum of the first 30 terms is:
Q29. The value of Σ (3k + 2) for k = 1 to 10 is:
Q30. The sum of the first n terms of an A.P. is 2n² + n. Its common difference is: