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Number series — find the next two terms of the sequence: 84, 78, 72, 66, 60, 54, 48

Difficulty: Easy

Correct Answer: 42 36

Explanation:


Introduction / Context:
This is a decreasing arithmetic progression, common in test questions. Recognizing the constant negative step enables quick extrapolation to the next terms without complicated calculations.


Given Data / Assumptions:

  • Sequence: 84, 78, 72, 66, 60, 54, 48
  • We need the next two values (positions 8 and 9).


Concept / Approach:
Find the common difference d by subtracting consecutive terms. For a descending AP, d will be negative, and we keep subtracting d to extend the series.


Step-by-Step Solution:

Common difference: 78 − 84 = −6 (constant across the list).Next term: 48 − 6 = 42.Term after that: 42 − 6 = 36.Therefore, the next two terms are 42 and 36.


Verification / Alternative check:

Mid-sequence confirmation: 66 − 6 = 60 and 60 − 6 = 54, consistent with d = −6.


Why Other Options Are Wrong:

44 34 / 42 32 / 40 34 / 38 32: These pairs deviate from the constant −6 step for one or both entries.


Common Pitfalls:

Switching to variable steps unnecessarily; the pattern is uniformly −6.


Final Answer:
42 36

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