If a, b, c, d are positive real numbers such that a, b, c, d form an increasing arithmetic sequence and a, b, d form a geometric sequence, then a/d is
a. 1/12
b. 1/6
c. ¼
d. 1/3
e. ½

A/d is equal to c/b if a, b, c, and d are positive real numbers that form an increasing arithmetic sequence and a, b, d, a geometric sequence.

Since a, b, c, d form an increasing arithmetic sequence, we can write them as

a = x,

b = x + d,

c = x + 2d

Also, since a, b, d form a geometric sequence, we have

a = bx, d = b2

Substituting the values in the equation for c and d, we get

c = x + 2b2

Now, dividing both sides by b, we get

a/d = c/b

=> a/d = (x + 2b2)/b

=> a/d = x/b + 2b

=> a/d = c/b

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If a, b, c, d are positive real numbers such that a, b, c, d form an increasing arithmetic sequence and a, b, d form a geometric sequence, then a/d is a. 1/12 b. 1/6 c. ¼ d. 1/3 e. ½

Answer :

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If a, b, c, d are positive real numbers such that a, b, c, d form an increasing arithmetic sequence and a, b, d form a geometric sequence, then a/d is
a. 1/12
b. 1/6
c. ¼
d. 1/3
e. ½