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Find the A.P after inserting two arithmetic means between two numbers which are arithmetic means of the sequences 1,2,3,4 and 5,6,7,8 respectively?

Asked by Topperlearning User 5th October 2016, 6:08 AM
Answered by Expert
Answer:

The first number is the arithmetic mean of 1,2,3,4 i.e. fraction numerator 1 plus 2 plus 3 plus 4 over denominator 4 end fraction equals 5 over 2

The second number is the arithmetic mean of 5,6,7,8 i.e. fraction numerator 5 plus 6 plus 7 plus 8 over denominator 4 end fraction equals 13 over 2

we need to insert two AMs between 5/2 and 13/2 after which the resulting sequence will be an AP with common difference given by fraction numerator begin display style 13 over 2 end style minus begin display style 5 over 2 end style over denominator 2 plus 1 end fraction equals 4 over 3

The first AM is 5/2+4/3=23/6

The second AM is 5/2+2(4/3)=31/6

The resulting AP is 5/2 , 23/6 , 31/6 , 13/2



Answered by Expert 5th October 2016, 8:08 AM
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