Question

If in an A.P. \(a_{30}-a_{20}=50\), then the common difference is

• A. \(4\)
• B. \(15\)
• C. \(5\)
• D. \(10\)

Hint:

In A.P., \(a_{m}-a_{n}=(m-n)d\). This is a shortcut for differences.

Answer 1

The Correct Option is C

Step 1: Write formulas.
\(a_{30}=a+29d,\;\;a_{20}=a+19d\).
Step 2: Subtract.
\[ a_{30}-a_{20}=(a+29d)-(a+19d)=10d \]
Step 3: Use condition.
\[ 10d=50 \quad \Rightarrow \quad d=5 \]