Question

If a, b, c and d are consecutive terms of an A.P., then c – b is equal to :

• A. d – a
• B. d – b
• C. d – c
• D. c – a

Hint:

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!

Answer 1

The Correct Option is C

Step 1: Use a concrete AP instead of pure symbols.
Take any AP with four consecutive terms, say $2, 5, 8, 11$, so $a=2, b=5, c=8, d=11$.
Step 2: Compute the quantity asked for.
$c - b = 8 - 5 = 3$.
Step 3: Check which option gives the same value.
$d - c = 11 - 8 = 3$, which matches. Checking $d-a=9$, $d-b=6$ and $c-a=6$ shows none of these equal $3$ in general.
\[ \boxed{c-b = d-c} \]