ECAT — Engineering College Admission Test (UET)
Take the ECAT Mathematics — Sequences and Series (Set 5): 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. In an A.P. the 5th term is 17 and the 9th term is 33. The 20th term is:
Answer: C. 77
Explanation: 4d = 33 − 17 = 16 gives d = 4, so a = 17 − 16 = 1 and a₂₀ = 1 + 19·4 = 77.
Q2. The sum of all multiples of 7 lying between 100 and 300 is:
Answer: C. 5586
Explanation: They run from 105 to 294, which is 28 terms. The sum is 28(105 + 294)/2 = 5586.
Q3. The sum of the integers from 1 to 100 that are divisible by neither 3 nor 5 is:
Answer: A. 2632
Explanation: Total 5050. Multiples of 3 sum to 1683, multiples of 5 to 1050, multiples of 15 to 315 (counted twice). So 5050 − 1683 − 1050 + 315 = 2632.
Q4. If four arithmetic means are inserted between 5 and 30, the third mean is:
Answer: D. 20
Explanation: There are 6 terms with common difference (30 − 5)/5 = 5: 5, 10, 15, 20, 25, 30. The third mean is 20.
Q5. In a G.P. the third term is 12 and the sixth term is 96. The eighth term is:
Answer: A. 384
Explanation: r³ = 96/12 = 8 so r = 2, a = 3, and a₈ = 3·2⁷ = 384.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. If 1 + 3 + 9 + … + 3ᵏ = 3280, the number of terms in the sum is:
Q7. The sum of the series Σ (2ⁿ + 3ⁿ)/6ⁿ from n = 1 to infinity is:
Q8. For which value of x does 1 + (1 − x) + (1 − x)² + … sum to 5?
Q9. The harmonic mean of 4 and 9 is:
Q10. In a harmonic progression the 5th term is 1/12 and the 11th term is 1/24. The 20th term is:
Q11. The sum of the squares of the first six odd positive integers, 1² + 3² + 5² + … + 11², is:
Q12. The value of 1·2 + 2·3 + 3·4 + … + 10·11 is:
Q13. The value of 1² − 2² + 3² − 4² + … − 10² is:
Q14. The sum of the series 1 + 2/2 + 3/4 + 4/8 + 5/16 + … (nth term n/2ⁿ⁻¹) is:
Q15. A sequence has a₁ = 1 and aₙ₊₁ = 2aₙ + 1. Then a₆ equals:
Q16. A sequence has a₁ = 1, a₂ = 3 and aₙ₊₂ = aₙ₊₁ + aₙ. The value of a₇ is:
Q17. Four numbers in A.P. have sum 32 and the sum of their squares is 276. The smallest of them is:
Q18. Three numbers in G.P. have sum 14 and product 64. The largest is:
Q19. If a, b, c are in A.P., which of the following triples must also be in A.P.?
Q20. The number of terms in the A.P. 7, 11, 15, …, 99 is:
Q21. In an A.P. the sum of the 5th and 15th terms is 40. The sum of the first 19 terms is:
Q22. The product of the first five terms of a G.P. whose third term is 8 is:
Q23. The number of terms in the G.P. 3, 6, 12, …, 768 is:
Q24. An infinite G.P. has a sum equal to four times its first term. Its common ratio is:
Q25. If x, y > 0 and x + y = 10, the minimum value of 1/x + 1/y is:
Q26. The harmonic mean of the three numbers 1, 2 and 4 is:
Q27. The value of 1/(1·2) + 1/(2·3) + 1/(3·4) + … + 1/(20·21) is:
Q28. The sum of the first four terms of 3 + 33 + 333 + 3333 + … is:
Q29. An A.P. has 10 terms, first term 2 and sum 200. Its common difference is:
Q30. In an A.P. the 2nd term is 1/3 and the 3rd term is 1/2. The sum of its first 6 terms is: