Arithmetic Progression (Missing Term)

Arithmetic Progression (AP) missing term problems present a sequence where one term is missing. You must find the missing term by identifying the common difference between consecutive terms.

10Worksheets
200+Practice Questions
BeginnerDifficulty
2-3 hoursHours to Master

Introduction to Arithmetic Progression (Missing Term)

Arithmetic Progression (AP) missing term problems present a sequence where one term is missing. You must find the missing term by identifying the common difference between consecutive terms.

Prerequisites

Arithmetic Progression concept Common difference formula: d = a₂ - a₁ nth term formula: aₙ = a₁ + (n-1)d Basic arithmetic
Why This Matters: AP missing term problems appear frequently in series sections. 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 (Missing Term) Problems

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Step 1: Identify two consecutive terms in the series (if available)

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

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Step 3: If the missing term is between known terms, use the AP formula

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Step 4: If the missing term is at position n, use aₙ = a₁ + (n-1)d

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Step 5: Calculate the missing term

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Step 6: Verify by checking if the term fits the sequence

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Step 7: Present the missing term

Pro Strategy: Always find the common difference first. If consecutive terms are not available, use any two known terms to find d = (a_m - a_n)/(m-n).

Example Problem

Example: Find the missing term: 5, 9, 13, ?, 21 Solution: Step 1: Known terms: 5, 9, 13, _, 21 Step 2: Common difference d = 9 - 5 = 4 Step 3: Check: 13 + 4 = 17 Step 4: Check further: 17 + 4 = 21 ✓ Step 5: Missing term = 17 Answer: 17

Pro Tips & Tricks

  • If missing term is between two known terms, it's the average of the two: a_missing = (a_left + a_right)/2
  • For evenly spaced terms, the middle term is the arithmetic mean of its neighbors
  • Common difference can be negative (decreasing sequence)
  • Check if the sequence has a constant difference between ALL consecutive terms
  • For larger gaps, use d = (a_last - a_first)/(n-1)
  • Always verify your answer by checking the sequence

Shortcut Methods to Solve Faster

Middle term = (First + Last)/2 for three-term AP
aₙ = a₁ + (n-1)d
d = (a_m - a_n)/(m-n)

Common Mistakes to Avoid

Using wrong position index (off-by-one errors)
Assuming increasing sequence when it might be decreasing
Not verifying the pattern with all given terms
Forgetting that d can be fractional

Exam Importance

Arithmetic Progression (Missing Term) 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 (Missing Term)?

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

20 practice questions
Detailed solutions
Step-by-step explanations
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