Question

Which of the following are in A.P.?

• A. \(0.4,\,0.44,\,0.444,\,\ldots\)
• B. \(1,\,11,\,111,\,\ldots\)
• C. \(2,\,4,\,8,\,16,\,\ldots\)
• D. \(0,\,-4,\,-8,\,-12,\,\ldots\)

Hint:

A sequence is an A.P. if the difference between consecutive terms is always the same.

Answer 1

The Correct Option is D

Step 1: Check sequence (1).
\(0.44-0.4=0.04,\;0.444-0.44=0.004\), not constant. Not an A.P.
Step 2: Check sequence (2).
\(11-1=10,\;111-11=100\), not constant. Not an A.P.
Step 3: Check sequence (3).
Differences \(4-2=2,\;8-4=4,\;16-8=8\), not constant. This is a G.P.
Step 4: Check sequence (4).
Differences \(-4-0=-4,\;-8-(-4)=-4,\;-12-(-8)=-4\), constant. Hence this is an A.P.