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If there are 11 arithmetic means between 20 and 80, identify t

Question

If there are $11$ arithmetic means between $20$ and $80$ , identify the value of the fourth mean.

40

45

60

32

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Evelyn Discussed

If there are

11

arithmetic means between

20

and

80

, identify the value of the fourth mean.

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Let the AM to be inserted between

20

and

80

are

A_{1}, A_{2}, A_{3}, .... A_{11}

Then we have the series

20, A_{1}, A_{2}, A_{3}, .... A_{11}, 80

forms an arithmetic progression

a_{n} = a + (n - 1) d

...... (

n^{t h}

term of AP)

80 = 20 + (13 - 1) d 60 = 12 d d = 5

4^{t h}

mean is

a_{5}

= a + 4 d = 20 + 4 \times 5 = 40

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Question Text	If there are $11$ arithmetic means between $20$ and $80$ , identify the value of the fourth mean.
Answer Type	Text solution:1
Upvotes	150