Sequences and Series — Engineering Board Exam Practice Questions

43 free engineering board exam reviewer questions on Sequences and Series (Algebra), each with the correct answer and a worked solution.

  1. Solve for x in the following equation: x+4x+7x+·s+64x=1430.
  2. The seating section in a Coliseum has 30 seats in the first row, 32 seats in the second row, 34 seats in the third row, and so on, until…
  3. Find the 100th term of the sequence 1.01, 1.00, 0.99,
  4. Determine x, so that x, 2x+7, 10x-7 will form a geometric progression.
  5. If one third of the air in a tank is removed by each stroke of an air pump, what fractional part of the total air is removed in 6 strokes?
  6. If the 1st term of the geometric progression is 27 and the 4th term is -1, the third term is:
  7. Find the ratio of an infinite geometric series if the sum is 2 and the first term is 1/2.
  8. A piece of paper is 0.05 inches thick. Each time the paper is folded into half, the thickness is doubled. If the paper was folded 12…
  9. What is the 11th term of the harmonic progression if the first and the third terms are 1/2 and 1/6 respectively?
  10. In a certain arithmetic progression, the twentieth term is 32 and the common difference is 3. Find the 3rd term.
  11. The 8th term of an arithmetic progression is 12 and the 39th term is 43. What is the sum of the first 30 terms?
  12. Find the arithmetic mean of -14, -12, -10, -4, -1, 5.
  13. There are seven arithmetic means between 3 and 35. Find the sum of all the terms.
  14. The arithmetic mean of 6 numbers is 17. If two numbers are added, the new set of numbers will have an arithmetic mean of 21. What are the…
  15. The 3rd and 8th terms of a geometric progression are 27 and 6561 respectively. Find the common ratio.
  16. Determine the value of x, so that x, 2x+4, 10x-4 will be a geometric progression.
  17. The sum of a geometric series is as follows: S=1.0+1.1+1.21+1.331+·s up to the 50th term. Find S.
  18. Find the sum of the infinite geometric series 1, -1/5, 1/25,
  19. There are four geometric means between 3 and 729. Find the fourth term of the resulting sequence.
  20. The geometric mean and arithmetic mean of two numbers are 8 and 17 respectively. Find the smaller (first) number.
  21. Two numbers differ by 40 and their arithmetic mean exceeds their geometric mean by 2. What are the numbers?
  22. In the series 0.5, 0.2, 0.125, (a harmonic progression), find the 20th term.
  23. The arithmetic mean of two numbers is 4 and their harmonic mean is 15/4. Find the smaller number.
  24. Find the fifth term of the series whose sum of the first n terms is 3n+2-6.
  25. Find the 10th term of the series 1, 5, 12, 22,
  26. The increasing sequence 1, 3, 4, 9, 10, 12, 13, consists of all positive integers which are powers of 3 or sums of distinct powers of 3…
  27. Find the value of a2+a4+a6+·s+a98 if a1, a2, a3, is an arithmetic progression with common difference 1, and a1+a3+a5+·s+a97=137.
  28. Let x1=97, x2=2/x1, x3=3/x2, x4=4/x3, , x8=8/x7. Find x1 · x2 ·s x8.
  29. The pages of a book are numbered 1 through n. When the page numbers of the book were added, one of the page numbers was mistakenly added…
  30. What is the first four terms of the sequence whose general term is n2+1?
  31. Find the sum of the first 5 terms in the sequence whose general term is 2n-1.
  32. Determine the 5th term of the sequence whose sum of n terms is given by (2n+3-5).
  33. Find the 30th term of the arithmetic progression 4, 7, 10,
  34. Four positive integers form an arithmetic progression. If the product of the 1st and the last term is 70 and the product of the 2nd and…
  35. How many terms of the progression 3, 5, 7, should there be so that their sum will be 2600?
  36. What is the sum of all odd integers between 10 and 500?
  37. What is the sum of all even integers from 10 to 500?
  38. The sum of an infinite geometric series is 18, and the sum of the squares of its terms is 108. Find the first term.
  39. Find the sum of the first 12 terms of the geometric sequence 3, 6, 12,
  40. A ball is dropped from a height of 12 m and rebounds to 23 of its previous height after each bounce. What total distance does it travel…
  41. Express the repeating decimal 0.363636 as a common fraction in lowest terms.
  42. Insert 4 arithmetic means between 5 and 30. What is the third mean?
  43. Find the 15th term of the arithmetic sequence 7, 11, 15,