Answer:
The rule for given sequence is: a_n = -27+16n
And the 100th term is: 1573
Step-by-step explanation:
Given sequence is:
-11, 5, 21, 37, 53, ...
Here

First of all, we have to find if this is an arithmetic sequence
For that purpose, the common difference has to be found. Common difference, denoted by d, is the difference between consecutive terms of an arithmetic sequence
So,

As the common difference is same, the sequence is an arithmetic sequence
General rule for arithmetic sequence is:

Putting values

For 100th term,
Putting n=100

Hence,
The rule for given sequence is: a_n = -27+16n
And the 100th term is: 1573
Question 23:
x = 4
DE = 44
Question 24:
x = 25
SE = 28
Step-by-step explanation:
As RS is the perpendicular bisector of DE, it will divide DE in two equal parts DS and SE
<u>Question number 23:</u>
Given
DS = 3x+10
SE = 6x-2
As the two segments are equal:

Subtracting 10 from both sides

subtracting 6x from both sides

Dividing both sides by -3

Now

And

<u>Question No 24:</u>
Given
DS = x+3
DE = 56
We know that:

So
DS = 
As DS is 28, SE will also be 28
Hence,
Question 23:
x = 4
DE = 44
Question 24:
x = 25
SE = 28
Keywords: Bisector, Line segment
Learn more about line segments at:
#LearnwithBrainly
Answer:
Infinite solution
Step-by-step explanation:
There is 3 possible solutions to a system of linear equations:
- One solution - two distinct lines that do not share y-intercept or slop intersect at a point
- No solution - two distinct lines that share the same slope but not the same y-intercept never intersect and are parallel
- Infinite solution - one distinct function represented two ways which in simplest form share the same slope and y-intercept
The first equation is in simplest form y=2x+3.
The second equation 2y=4x+6 when simplified becomes y=2x+3.
These are the same lines with the same slope and y-intercept. Therefore, they have infinite solutions.
Answer:
19th term = ar^18
19th term = 774,840,978
Step-by-step explanation:
First term, a = 2
Common ratio, r = 3
nth term of a geometric sequence = ar^(n-1)
19th term = ar^(19-1)
19th term = ar^18
= 2 × 3^18
= 2 × 387,420,489
= 774,840,978
19th term = 774,840,978