If n arithmetic means are inserted between a and b, then the common difference is ……………….
If n arithmetic means are inserted between a and b, then the common difference is ……………….
A) a + b/n + 1
B) n + 1/b + a
C) n + 1/b - a
D) b - a/n + 1
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Correct option is (D) b-a/n+1
Let a+d, a+2d, .........., a+nd are n arithmetic means inserted between a and b.
\(\therefore\) a, a+d, a+2d, .........., a+nd, b will form an A.P.
\(\therefore\) \(a+(n+1)d=b\)
\(\Rightarrow(n+1)d=b-a\)
\(\Rightarrow\) \(d=\frac{b-a}{n+1}\)
\(\therefore\) Common difference is \(d=\frac{b-a}{n+1}.\)
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