A finite arithmetic sequence has 12 termsThe last term is 100 and the common difference is 3. What is the first term?

67

Step-by-step explanation:

From the question given above, the following data were obtained:

Number of terms (n) = 12

Last term (L) = 100

Common difference (d) = 3

First term (a) =?

We can obtain the first term of the arithmetic sequence as follow:

L = a + (n – 1)d

100 = a + (12 – 1)3

100 = a + (11)3

100 = a + 33

Collect like terms

100 – 33 = a

a = 67

Therefore, the first term of the arithmetic sequence is 67

∠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.

their is no graph showing

step-by-step explanation: