+0

# Algebra

0
2
1
+1859

When the same constant is added to the numbers 60, 120, and 160, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

Jun 15, 2024

#1
+1280
+1

Let's set variables in order to solve this problems.

Let's let c be the constant added to each number.

We get $$60+c, 120+c, 160+c$$

Since all the terms form an geometric series, we can write the formula

$$\frac{60+c}{120+c} = \frac{120+c}{160+c}$$

Now, we simplfy solve for c.

$$(c+160)(60+c)=(c+120)(120+c)$$

Distributing everything, combining all like terms, and moving everything to one side, we get

$$-20c-4800=0$$

$$c=-240$$

We plug this back in, and we get the series $$-180, -120, -80$$

This has a common ratio of $$180/120=3/2$$

So 3/2 is our answer,

Thanks! :)

Jun 15, 2024

#1
+1280
+1

Let's set variables in order to solve this problems.

Let's let c be the constant added to each number.

We get $$60+c, 120+c, 160+c$$

Since all the terms form an geometric series, we can write the formula

$$\frac{60+c}{120+c} = \frac{120+c}{160+c}$$

Now, we simplfy solve for c.

$$(c+160)(60+c)=(c+120)(120+c)$$

Distributing everything, combining all like terms, and moving everything to one side, we get

$$-20c-4800=0$$

$$c=-240$$

We plug this back in, and we get the series $$-180, -120, -80$$

This has a common ratio of $$180/120=3/2$$

So 3/2 is our answer,

Thanks! :)

NotThatSmart Jun 15, 2024