MathDB

Suppose we have four real numbers

a,b,c,d

such that

a

is nonzero,

a,b,c

form a geometric sequence, in that order, and

b,c,d

form an arithmetic sequence, in that order. Compute the smallest possible value of

\frac{d}{a}.

(A geometric sequence is one where every succeeding term can be written as the previous term multiplied by a constant, and an arithmetic sequence is one where every succeeeding term can be written as the previous term added to a constant.)

Problem Statement