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Algebra Exercises: Arithmetic, Geometric, and Harmonic Progressions, Exercises of Algebra

Pamantasan ng Lungsod ng Maynila (PLM)Algebra

Math Algebra Exercises and Answers

Typology: Exercises

2020/2021

Uploaded on 10/06/2021

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NCE 4101 – CE Integration 1 – Algebra Part 3
IX. ARITHMETIC PROGRESSION
36. The 7th term of an arithmetic sequence is
34 while the 11th term is 286. What is the
24th term? What term is 727? What is the
sum of the first 200 terms?
37. Insert 7 arithmetic means between 69 and
93.
38. How many numbers divisible by 4 lie
between 70 and 203?
39. What is the sum of all odd integers between
10 and 500?
40. Determine x so that 2x + 1, 10x - 15, 2x^2 +
9 will be an arithmetic progression
X. GEOMETRIC PROGRESSION
41. The 7th term of a geometric progression is
34 while the 11th term is 544. What is the
24th term? What term is 17,408? What is
the sum of the first 200 terms?
42. Insert 4 geometric means between 2,048
and 2
43. Find the geometric mean of 2, 7, 9, 11.
XI. HARMONIC PROGRESSION
44. The second and fourth term of a harmonic
progression is 5/4 and - 8. Find the 6th
term.
45. The geometric mean and the arithmetic
mean of two numbers are 8 and 17,
respectively. Find the harmonic mean.
46. It took a certain vehicle 3 hours to travel a
distance of 120 km. On its way back, it took
him only 2 hours to travel the same path.
What was his average speed? (space mean
speed)
XIII. DIOPHANTINE EQUATION
47. Find the value of x in the equation 14 x +
35y = 91. Assume x and y are both positive
integers. a) 5 b) 3 c) 6 d) 4
48. Three items A, B and C were sold in a store.
Item A costs P 10.00 each, item B costs P
1.00 each and three pieces of item C cost
P1.00. The total sales at the end of the day
were P100.00 and a total of 100 items were
sold. How many of item B were sold? a) 42
b) 40 c) 54 d) 49
XIV. NUMBER / DIGIT PROBLEMS
49. The sum of the digits of a three-digit
number is 17. If the digits are reversed and
the resulting number is added to the
original number, the result is 1,474. If the
resulting number is subtracted from the
original number the result is 396. Find the
original number.
50. The sum of the digits of a 2-digit number is
10. If the number is divided by the units
digit, the quotient is 3 and the remainder is
4. Find the number.
pf2

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NCE 4101 – CE Integration 1 – Algebra Part 3

IX. ARITHMETIC PROGRESSION

  1. The 7th term of an arithmetic sequence is 34 while the 11th term is 286. What is the 24th term? What term is 727? What is the sum of the first 200 terms?
  2. Insert 7 arithmetic means between 69 and
  3. How many numbers divisible by 4 lie between 70 and 203?
  4. What is the sum of all odd integers between 10 and 500?
  5. Determine x so that 2x + 1, 10x - 15, 2x^2 + 9 will be an arithmetic progression X. GEOMETRIC PROGRESSION
  6. The 7th term of a geometric progression is 34 while the 11th term is 544. What is the 24th term? What term is 17,408? What is the sum of the first 200 terms?
  7. Insert 4 geometric means between 2, and 2
  8. Find the geometric mean of 2, 7, 9, 11. XI. HARMONIC PROGRESSION
  9. The second and fourth term of a harmonic progression is 5/4 and - 8. Find the 6th term.
  10. The geometric mean and the arithmetic mean of two numbers are 8 and 17, respectively. Find the harmonic mean.
  11. It took a certain vehicle 3 hours to travel a distance of 120 km. On its way back, it took him only 2 hours to travel the same path. What was his average speed? (space mean speed)

XIII. DIOPHANTINE EQUATION

  1. Find the value of x in the equation 14 x + 35y = 91. Assume x and y are both positive integers. a) 5 b) 3 c) 6 d) 4
  2. Three items A, B and C were sold in a store. Item A costs P 10.00 each, item B costs P 1.00 each and three pieces of item C cost P1.00. The total sales at the end of the day were P100.00 and a total of 100 items were sold. How many of item B were sold? a) 42 b) 40 c) 54 d) 49 XIV. NUMBER / DIGIT PROBLEMS
  3. The sum of the digits of a three-digit number is 17. If the digits are reversed and the resulting number is added to the original number, the result is 1,474. If the resulting number is subtracted from the original number the result is 396. Find the original number.
  4. The sum of the digits of a 2-digit number is
  5. If the number is divided by the units digit, the quotient is 3 and the remainder is
  6. Find the number.