BRAINLEST! please help
Identify the formula for finding the nth term of an arithmetic sequence, where A(n) is the nth term of an arithmetic sequence, a is the first term, n is the term number and d is the common difference.

Option D: A(n) = a + (n – 1) d

Solution:

To identify the formula for finding the nth term of an arithmetic sequence.

Let a be the first term.

d be the common difference of the each term.

n be the term of the number.

A(n) be the nth term of the arithmetic sequence.

Arithmetic formula:

A(n) = a + (n – 1) d

Example: 1, 4, 7, 10, 13, 16, 19, ...

This is a arithmetic sequence.

a = 1, d = 4 – 1 = 3.

To find the 5th term:

Substitute this in the above formula, we get

A(n) = a + (n – 1) d

A(5) = 1 + (5 – 1) 3

       = 1 + 4(3)

       = 1 + 12

A(5) = 13

In the given sequence 5th term is 13.

Hence Option D is the correct answer.

A(n) = a + (n – 1) d

∠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.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x