# Question #39a8d

Mar 5, 2016

#### Explanation:

${x}_{2} + {x}_{4} = 104$
${x}_{2} - {x}_{4} = 40$

so, adding member to member the two equations:

$2 {x}_{2} = 144 \Rightarrow {x}_{2} = 72$

and

${x}_{4} = 72 - 40 = 32$.

The geometric sequence is a sequence in which the ratio between two consecutive numbers is constant ($= q$).

So:

${x}_{4} = {x}_{3} \cdot q = \left({x}_{2} \cdot q\right) \cdot q = {x}_{2} \cdot {q}^{2}$,

then:

${q}^{2} = {x}_{4} / {x}_{2} = \frac{32}{72} = \frac{4}{9} \Rightarrow q = \frac{2}{3}$, ($q$ is a positive number!)

and:

${x}_{2} = {x}_{1} \cdot q \Rightarrow {x}_{1} = {x}_{2} / q = 72 \cdot \frac{3}{2} = 108$.