Test Index

Sequence and Series

Question : 79 of 86

Marks: +1, -0

If three AM's between 3 and 11 , they are

Solution:

Concept:

Arithmetic means between two numbers form an arithmetic progression (AP) with the given numbers as first and last terms.

Explanation:

Let the three arithmetic means between

3

and

11

A_1

A_2

A_3

Then the sequence is

3, A_1, A_2, A_3, 11

, which has

5

terms in AP.

First term

a = 3

, fifth term

a + 4d = 11

3 + 4d = 11 \implies 4d = 8 \implies d = 2

Thus the means are:

A_1 = 3+2 = 5

A_2 = 3+4 = 7

A_3 = 3+6 = 9

Answer:

5, 7, 9

(Option C).

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