ReasoningAbility.com

Arithmetic Progression

Arithmetic Progression (AP) problems present sequences where each term increases or decreases by a fixed constant called the common difference. These fundamental problems test your ability to identify linear patterns and extend sequences using the formula aₙ = a₁ + (n-1)d.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Arithmetic Progression

Arithmetic Progression (AP) problems present sequences where each term increases or decreases by a fixed constant called the common difference. These fundamental problems test your ability to identify linear patterns and extend sequences using the formula aₙ = a₁ + (n-1)d.

Prerequisites

Basic addition and subtraction Understanding of constant difference Position-to-term relationship nth term formula
Why This Matters: Arithmetic Progression problems are the most common sequence type. You can expect 2-3 questions in SSC CGL, 2-3 in Banking PO, and 2-3 in Railways RRB exams.

How to Solve Arithmetic Progression Problems

1

Step 1: Identify the first term (a) and second term of the sequence

2

Step 2: Calculate the common difference: d = a₂ - a₁

3

Step 3: Verify the difference is constant for all consecutive terms

4

Step 4: For next term: add d to the last term

5

Step 5: For missing term: use aₙ = a₁ + (n-1)d

6

Step 6: For wrong term identification: find where the difference breaks pattern

7

Step 7: Verify your answer by checking consistency with the sequence

Pro Strategy: Always calculate the common difference first. The difference between any two consecutive terms must be constant. For missing terms, use the formula or find the average of surrounding terms.

Example Problem

Example: Find the next term in the sequence: 5, 9, 13, 17, ___ Solution: Step 1: First term a = 5, second term = 9 Step 2: Common difference d = 9 - 5 = 4 Step 3: Check: 13-9=4, 17-13=4 ✓ Step 4: Next term = 17 + 4 = 21 Answer: 21

Pro Tips & Tricks

  • Common difference d = a₂ - a₁ = a₃ - a₂
  • nth term formula: aₙ = a₁ + (n-1)d
  • If the sequence is decreasing, d is negative
  • The sum of n terms: Sₙ = n/2 × (2a + (n-1)d)
  • Three terms in AP can be written as a-d, a, a+d
  • The middle term of an odd-length AP is the average of all terms

Shortcut Methods to Solve Faster

Next term = Last term + Common difference
Missing term = (Previous term + Next term) / 2 (for middle term)
d = (aₘ - aₙ)/(m - n)
For 3 terms: middle term = (first + last)/2

Common Mistakes to Avoid

Using the wrong sign for common difference in decreasing sequences
Adding difference to the wrong term position
Confusing AP with geometric progression
Not verifying the pattern with all given terms

Exam Importance

Arithmetic Progression is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Arithmetic Progression?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now