Question

If `a/b = b/c = c/d`, then `(b^3 + c^3 + d^3)/(a^3 + b^3 + c^3)` is equal to ______.

Options

• `a/b`

• `b/c`

• `c/d`

• `d/a`

Answer 1

If `a/b = b/c = c/d`, then `(b^3 + c^3 + d^3)/(a^3 + b^3 + c^3)` is equal to `underlinebb(d/a)`.

Explanation:

Let a, b, c, d be proportional terms in a geometric sequence. The denominator is a factor of `a^3/d^3` larger than the numerator, so their ratio is `d^3/a^3`; equivalently, the ratio of the sums is `d/a`. Thus option d is correct.