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GrogVix [38]
3 years ago
8

If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields

Mathematics
1 answer:
almond37 [142]3 years ago
6 0

You're looking for a number <em>w</em> such that the numbers

{1 + <em>w</em>, 7 + <em>w</em>, 15 + <em>w</em>}

form a geometric sequence, which in turn means there is a constant <em>r</em> for which

7 + <em>w</em> = <em>r</em> (1 + <em>w</em>)

15 + <em>w</em> = <em>r</em> (7 + <em>w</em>)

Solving for <em>r</em>, we get

<em>r</em> = (7 + <em>w</em>) / (1 + <em>w</em>) = (15 + <em>w</em>) / (7 + <em>w</em>)

Solve this for <em>w</em> :

(7 + <em>w</em>)² = (15 + <em>w</em>) (1 + <em>w</em>)

49 + 14<em>w</em> + <em>w</em> ² = 15 + 16<em>w</em> + <em>w</em> ²

2<em>w</em> = 34

<em>w</em> = 17

Then the three terms in the sequence are

{18, 24, 32}

and indeed we have 24/18 = 4/3 and 32/24 = 4/3.

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