What are the first four terms of a geometric sequence if its common ratio is 5 and its first term is 2.5? 2.5, 7.5, 12.5, 17.5
2.5, 0.5, 0.1, 0.02
2.5, 12.5, 62.5, 312.5
2.5, -2.5, -7.5, -12.5

 C:  2.5, 12.5, 62.5, 312.5

Step-by-step explanation:

Let us remember that in a geometric sequence:

    ratio =

We know that (first term) is 2.5.  So plug in the numbers into the above formula:

    5 =

Multiply both sides by 2.5 to solve for (second term):

    5 × 2.5 = 12.5

By process of elimination, it is obvious the correct answer is C.

We can double check your answer by checking the rate is 5 by dividing:

   For example, 62.5 () divided by 12.5 () is appropriately 5.  

   Similarly, 312.5 () divided by 32.5 () is again 5, confirming our answer to be correct.

answer: 0+0=0

step-by-step explanation:

that is the only answer that can make 0

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.