What is the nth term in the sequence:
4, 7, 12, 19, 28
Please show working out
Answers
Explanation:
We find the first differences between terms:
7-4=3; 12-7=5; 19-12=7; 28-19=9.
Since these are different, this is not linear.
We now find the second differences:
5-3=2; 7-5=2; 9-7=2.
Since these are the same, this sequence is quadratic.
We use (1/2a)n², where a is the second difference:
(1/2*2)n²=1n².
We now use the term number of each term for n:
4 is the 1st term; 1*1²=1.
7 is the 2nd term; 1*2²=4.
12 is the 3rd term; 1*3²=9.
19 is the 4th term; 1*4²=16.
28 is the 5th term: 1*5²=25.
Now we find the difference between the actual terms of the sequence and the numbers we just found:
4-1=3; 7-4=3; 12-9=3; 19-16=3; 28-25=3.
Since this is constant, the sequence is in the form (1/2a)n²+d;
in our case, 1n²+d, and since d=3, 1n²+3.
Answer:
The nth term in the given sequence will be:
Step-by-step explanation:
We are given a sequence as:
4,7,12,19,28,....
Let represents the nth term in the sequence.
i.e.
i.e. these terms could also be written as:
Hence the nth term in the given sequence will be:
Related Questions
In how many ways can 10001 be written as the sum of two primes?a.0 b.1 c.2 d.3 e.4
What is the median of these numbers?4, 18, 20A 8® 12© 140 18
Bobby made cookies. the circumference of cookies are 6 cm. what is the diameter of the cookies?
Which graph shows the solution to the system of linear inequalities? y < 2x – 5 y > –3x + 1
Answers
Step-by-step explanation:
Answer:
Step-by-step explanation: a + ( n- 1 )d
where,
'a' means first term
'n' means number
'd' means common difference
Answers
Answer:
{-2/7, 2/7}
Step-by-step explanation:
Here you're being asked to solve the given equation 49w^2-4=0 for w with the hint that the solutions are fractions.
49w^2-4=0 is the product of the sum and difference of two squares:
(7w - 2)(7w + 2) = 0
Setting each factor equal to zero and solving for w, we get:
{-2/7, 2/7} as the solutions.
Answers
A. 26 7/12
B. 30 7/12
C. 42 1/12
D. 43 1/12
Answers
The solution is, the original roll of paper was 43 1/12 in. long.
the correct option is, D. 43 1/12.
What is addition?
Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
given that,
Sami cut 6 3/4 inches off a long roll of paper.
If the roll is now 36 1/3 inches long,
i.e. cut paper = 27/4 in.
remaining paper = 109/3 in.
so, we get,
total paper = 27/4 + 109/3
= 27*3 + 109*4 / 12
=517/12
=43 1/12
Hence, The solution is, the original roll of paper was 43 1/12 in. long.
the correct option is, D. 43 1/12.
To earn more on addition click:
#SPJ6
y=4x – 6
Select all statements about Xin's graph that are true.
The graph is a curved line.
The line passes through the origin.
The line passes through the point (0,6)
The slope of the line is 4
The y-intercept of the line is
–6
Answers
The solutions are
- The slope of the line is 4
- The y-intercept of the line is –6
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y coordinate of second point
y₁ = y coordinate of point one
m = slope
x = x coordinate of second point
x₁ = x coordinate of point one
Given data ,
Let the equation be y = 4x - 6
Now , the equation is of the form y = mx + b where m is the slope and b is the y-intercept
Therefore , the slope of the equation is m = 4
And the y intercept is -6
Hence , The slope of the line and the y-intercept of the line is –6
To learn more about equation of line click :
#SPJ2
y=mx+c where m is slope n c is y-intercept
y=4x-6
so the ans are:\
The slope of the line is 4
The y-intercept of the line is –6
simplify the expression
(16y^5/4y^3)^12
or
(16y54y3)12
Answers
Answer:
If this is for the k12 test then it is 2y.
I just took the test.
Answer:
4y^14
Step-by-step explanation:
you would look at the equation, and because it seems to be a division problem inside the ( ) then you would find the difference of the exponents. and divide the numbers in front of y. So, it would go from (16y^5/ 4y^3)^12, to (4y^2)^12. Then, you would add the exponents because it is multiplication. So you would get 4y^14.