Question

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

Answer 1

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 \(d=\frac{b-a}{n+1}.\)

Answer 2

Correct option is D) b - a/n + 1