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Progression Practice Test 1

Question : 20 of 23

Marks: +1, -0

Insert three arithmetic means between 11 and 12:

Solution: 👈: Video Solution

Concept:

To insert

n

arithmetic means between

a

and

b

, form an AP and use common difference

d=\frac{b-a}{n+1}

Explanation:

Let the three means be

x_1, x_2, x_3

The AP is

11, x_1, x_2, x_3, 12

There are

4

equal gaps from

11

12

So,

d=\frac{12-11}{3+1}=\frac{1}{4}

Thus,

x_1=11+\frac{1}{4}=\frac{45}{4}

x_2=11+2\left(\frac{1}{4}\right)=\frac{46}{4}=\frac{23}{2}

x_3=11+3\left(\frac{1}{4}\right)=\frac{47}{4}

These values are not present in options A to D.

Answer:

\frac{45}{4}, \frac{23}{2}, \frac{47}{4}

; so option E is correct.

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