Question

The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one. Then the common difference of the progression is

• A. \(2\)
• B. \(3\)
• C. \(\dfrac{3}{2}\)
• D. -1

Hint:

Translate word conditions directly into term equations.

Answer 1

The Correct Option is A

Let first term a, common difference d.
Step 1: Fourth term: a+3d=3a ⟹ 3d=2a (1)
Step 2: Seventh term condition: a+6d=2(a+2d)+1 ⟹ -a+2d=1 (2)
Step 3: From (1), a=(3d)/(2). Substituting in (2): -(3d)/(2)+2d=1 ⟹ d=2