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Class 10 › Mathematics › Arithmetic Progressions
CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
The $n^{th}$ term of an A.P. is $\sqrt{2}\,n+1$. Its common difference is
A. $\sqrt{2}$
B. $\sqrt{2}\,n$
C. $1$
D. $\sqrt{2}+1$
✅ Answer & Solution
✅ Correct Answer: A
Step 1: Given $a_n=\sqrt{2}\,n+1$.
Step 2: $a_1=\sqrt{2}(1)+1=\sqrt{2}+1$ and $a_2=\sqrt{2}(2)+1=2\sqrt{2}+1$.
Step 3: Common difference $$d=a_2-a_1=(2\sqrt2+1)-(\sqrt2+1)=\sqrt2$$
Step 4: (Shortcut: if $a_n=An+B$, then $d=A$, the coefficient of $n$.)
Answer: (A) $\sqrt{2}$
