Question:
If a, b, c and d are consecutive terms of an A.P., then c – b is equal to :
If a, b, c and d are consecutive terms of an A.P., then c – b is equal to :
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In any A.P., the common difference is defined as:
\[ a_{k} - a_{k-1} = \text{constant} \]
Thus, the difference between any two adjacent terms is identical!
\[ a_{k} - a_{k-1} = \text{constant} \]
Thus, the difference between any two adjacent terms is identical!
Updated On: Jul 9, 2026
- d – a
- d – b
- d – c
- c – a
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The question asks for an equivalent expression for the difference of consecutive terms \(c - b\) in an arithmetic progression.
Step 2: Key Formula or Approach:
By definition of an Arithmetic Progression (A.P.), the difference between any two consecutive terms is constant and is equal to the common difference (\(d\)):
\[ d = b - a = c - b = d - c \]
Step 3: Detailed Explanation:
• Let the consecutive terms of the A.P. be \(a, b, c, d\).
• The difference between the second and first term is:
\[ b - a = \text{common difference} \]
• The difference between the third and second term is:
\[ c - b = \text{common difference} \]
• The difference between the fourth and third term is:
\[ d - c = \text{common difference} \]
• Since all of these differences are equal to the common difference, we can write:
\[ c - b = d - c \]
Step 4: Final Answer:
The term \(c - b\) is equal to \(d - c\).
The question asks for an equivalent expression for the difference of consecutive terms \(c - b\) in an arithmetic progression.
Step 2: Key Formula or Approach:
By definition of an Arithmetic Progression (A.P.), the difference between any two consecutive terms is constant and is equal to the common difference (\(d\)):
\[ d = b - a = c - b = d - c \]
Step 3: Detailed Explanation:
• Let the consecutive terms of the A.P. be \(a, b, c, d\).
• The difference between the second and first term is:
\[ b - a = \text{common difference} \]
• The difference between the third and second term is:
\[ c - b = \text{common difference} \]
• The difference between the fourth and third term is:
\[ d - c = \text{common difference} \]
• Since all of these differences are equal to the common difference, we can write:
\[ c - b = d - c \]
Step 4: Final Answer:
The term \(c - b\) is equal to \(d - c\).
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