1.

Common difference of x + 4x/3 + 5x/3 + 2x + ..............isA) x/3B) 1/3C) x D) 2x/3

Answer»

Correct option is (A) x/3

Given sequence is \(x,\frac{4x}{3},\frac{5x}{3},2x,.......\)

\(\therefore a_1=x,a_2=\frac{4x}{3},a_3=\frac{5x}{3},a_4=2x\)

Now, \(a_2-a_1=\frac{4x}3-x\)

\(=\frac{4x-3x}3=\frac x3,\)

\(a_3-a_2=\frac{5x}3-\frac{4x}3=\frac{x}3\)

\(a_4-a_3=2x-\frac{5x}3\)

\(=\frac{6x-5x}3=\frac x3\)

\(\because\) \(a_4-a_3\) \(=a_3-a_2\) \(=a_2-a_1\) \(=\frac{x}{3}\)

\(\therefore\) Common difference \(=a_4-a_3=a_3-a_2=a_2-a_1=\frac x3\)

Correct option is A) x/3



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