Answer:
= - 3n
Step-by-step explanation:
There is a common difference between consecutive terms, that is
- 6 - (- 3) = - 9 - (- 6) = - 12 - (- 9) = - 3
This indicate the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 3 and d = - 3 , thus
= - 3 - 3(n - 1) = - 3 - 3n + 3 = - 3n
The n th term is - 3n
Answer:
<u>There are 17 terms in the sequence</u>
Step-by-step explanation:
<u>Arithmetic Sequence
</u>
An arithmetic sequence is a list of numbers with a definite pattern by which each term is calculated by adding or subtracting a constant number called common difference to the previous term. If n is the number of the term, then:
Where an is the nth term, a1 is the first term, and r is the common difference.
In the problem at hand, we are given the first term a1=13, the last term an=-23, and the common difference r=-2 1/4. Let's solve the equation for n:
We need to express r as an improper or proper fraction:
Substituting:
n=17
There are 17 terms in the sequence
Let's consider two prime numbers where each is larger than 2
Say the primes 7 and 11. Adding them gets us 7+11 = 18. This counter example disproves the initial claim since 18 = 9*2 = 6*3 making 18 composite (not prime)
In general, if we let p and q be two primes such that q > p > 2 and q is the next prime after p, then p and q are both odd. If any of them were even then they wouldn't be prime (2 would be a factor)
Adding any two odd numbers together leads to an even number
Proof:
p = 2k+1 where k is some integer
q = 2m+1 where m is some integer
p+q = 2k+1+2m+1 = 2(k+m) + 2 = 2(k+m+1) which is in the form of an even number
That proof above shows us that adding any prime larger than 2 to its next prime up leads to an even number. This further shows us that the claim is false overall. It is only true if you restrict yourself to the primes 2 and 3, which add to 5. Otherwise, the claim is false.
Answer:
4x2,3x3,1x6,
Step-by-step explanation:
Answer:
30 minutes
Step-by-step explanation:
If we have 2 points, we can find the slope
m = (y2-y1) / (x2-x1)
(0,24) and (5,20)
m = (20-24)/(5-0)
= -4/5
We know the y intercept (where x=0) (0,24)
We can write an equation for the line in y =mx+b
y = -4/5x+24
We want y = 0 (when the diameter is 0)
0 = -4/5 x +24
Subtract 24 from each side
-24 = -4/5 x +24-24
-24 = -4/5 x
Multiply each side by -5/4 to get x alone
-5/4 * -24 = -5/4 * -4/5 x
30 = x
