Question

Find the value of K such that 2/3,k,5/8 are the three consecutive terms of an Arithmatic progression

Answer 1

k - 2/3 = 5/8-k
2k = 5/8+2/3
2 k = 15+16/24
2k = 31/24
k = 31/48

Answer 2

Difference between the consecutive terms of AP can't be changed, which is also known as Common Difference.




Therefore :


Difference between 5 / 8 and k is equal to the difference between k and 2 / 3



5 / 8 - k = k - 2 / 3


5 / 8 + 2 / 3 = k + k


{ 3( 5 ) + 8( 2 ) } / 24 = 2k


{ 15 + 16 } 24 = 2k


31 / 24 = 2k


31 / ( 24 × 2 ) = k


31 / 48 = k





Therefore the value of k satisfying the given AP is 31 / 48

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