Question

if 2/3,k,5k/8 are in A.P find the value of k

Answer 1

If 2/3,k,5k/8 are in A.P then there is a common difference between them. Let the common difference be 'd'
i.e k+d=5k/8
=> d=-3k/8
i.e (2/3)+d=k
=> (2/3)+(3k/8)=k
=> (16-9k)/24=k
=> 16-9k=24k
=> 24k+9k=16
=> 33k=16
=> k=16/33
Therefore the value of k is 16/33
The series is 2/3,16/33,10/33

Answer 2

Since 2/3, k, 5k/8 are in A.P. then,
k-2/3=5k/8-k
or, (3k-2)/3=(5k-8k)/8
or, (3k-2)/3=-3k/8
or, 24k-16=-9k
or, 24k+9k=16
or, 33k=16
or, k=16/33 Ans.