42
let the smallest even number be x, than the four even numbers are x, x+2, x+4, x+6, their sum is 180
x+x+2+x+4+x+6=180
4x+12=180
4x=168
x=42
the smallest even number is 42.
Question:
Consider the sequence of numbers: 
Which statement is a description of the sequence?
(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.
(B) The sequence is recursive and can be represented by the function
f(n + 1) = f(n) + 3/8 .
(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .
(D) The sequence is arithmetic and can be represented by the function
f(n + 1) = f(n)3/8.
Answer:
Option B:
The sequence is recursive and can be represented by the function

Explanation:
A sequence of numbers are

Let us first change mixed fraction into improper fraction.

To find the pattern of the sequence.
To find the common difference between the sequence of numbers.




Therefore, the common difference of the sequence is 3.
That means each term is obtained by adding
to the previous term.
Hence, the sequence is recursive and can be represented by the function
Answer:

Step-by-step explanation:
1. Find the GCF (Greatest Common Factor)

2. Factor out the GCF and simplify.

3. Factor 
Which two numbers add up to -1 and multiply to -6?
<u>-3 and 2</u>
Rewrite the expression using the numbers above.

4. Done!

Answer:
30 more students
Step-by-step explanation:
690 + 30 = 720
720 / 9 = 80
Answer: 2343 / 256
Explanation
I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.
1) Adding the terms:
4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0
= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =
= 2343 / 256
2) Using the formula:
n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0
Here n - 1 = 4 => n = 5
r = 3/4
A = 3
Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =
= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =
= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256
So, no doubt, the answer is 2343 / 256