Test Index

Sequence and Series

Question : 81 of 86

Marks: +1, -0

The two arithmetic means between 4 and 13 are

Solution:

Concept:

Insert arithmetic means between two numbers by finding the common difference of the arithmetic sequence.

Explanation:

Let the two arithmetic means be

a

and

b

The sequence is

4, a, b, 13

(4 terms).

For an arithmetic progression,

a_n = a_1 + (n-1)d

Here

a_1 = 4

n = 4

a_4 = 13

13 = 4 + (4-1)d

⇒

13 = 4 + 3d

⇒

3d = 9

⇒

d = 3

Then

a = 4 + d = 7

and

b = 4 + 2d = 10

Answer:

7

and

10

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