The common difference in an arithmetic progression (A.P.) is the constant value added to each term to get the next term. It represents the fixed increase or decrease between consecutive terms in the sequence and remains unchanged throughout the progression.
An arithmetic progression (A.P.) is a sequence where each term differs from the previous term by a constant value. The fixed difference between consecutive terms is called common difference. The chapter covers finding nth term first term last term sum of n terms and applications in real-life scenarios through various problem-solving methods.
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The given sequence is 1/2q, (1-2q)/2q, (1-4q)/2q, …
To find true common difference, let’s analyze the pattern:
Looking at numerators: 1, (1-2q), (1-4q)
Denominator remains constant: 2q
In numerator:
From 1st to 2nd term: difference is -2q
From 2nd to 3rd term: difference is -2q
Since denominator is 2q,
Common difference = (-2q)/(2q) = 2q
This can be verified:
Starting with first term 1/2q:
– Add 2q: gives (1-2q)/2q (second term)
– Add 2q again: gives (1-4q)/2q (third term)
Hence, 2q is the correct answer.
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