Find the value of 'k' such that 2/3,k,5/8 are three consecutive terms of an AP.
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Answer:
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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