Answer:
Recursive:

Explicit:

And the 20th term is 225.
Step-by-step explanation:
We have the sequence:
35, 45, 55, 65.
Notice that each subsequent term is 10 more than the previous term.
Therefore, our common difference is (+)10.
Recursive Rule:
The standard format for the recursive rule is:

Where a is the initial term and d is the common difference.
From our sequence, we know that a the initial term is 35.
And as determined, our common difference d is 10.
Substitute. Hence, our recursive rule is:

Explicit Rule:
The standard format for the explicit rule is:

Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:

Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:

Evaluate:

Hence, the 20th term is 225.
Answer:
h=6
Step-by-step explanation:
a=b x h x 0.5
9=3 x h x 0.5
9/3=3/.5=6
h=6
Answer:
1/625
Step-by-step explanation:
When you multiply, you add the exponents. You now have
. This is equivalent to
which equals 1/625.
Answer:
210 cm³
Step-by-step explanation:
volume = W x L x H
(where W = width, L = length and H = height)
By inspection of the diagram,
W = 6 cm
L = 7 cm
H = 5 cm
Therefore, volume = 6 x 7 x 5 = 210 cm³
Answer: 5¹ + 5² + 5³, 130 students
<u>Step-by-step explanation:</u>
Monday: 1 1 1 1 1 = 5 ⇒ 5¹
+ Tuesday: 1(5) 1(5) 1(5) 1(5) 1(5) = + 25 ⇒ 5²
+ Wednesday:5(5) 5(5) 5(5) 5(5) 5(5) = <u>+125 </u>⇒ 5³
130
Extra Credit: How many students will know the rumor on Thursday? 5¹ + 5² + 5³ + 5⁴