(1,2), (2,9),(3,20).....
a) Determine what kind of growth this is and explain how you know.
b) Explain how you can go about finding an expression for the number of small squares in the nth term.
c)What is the expression for the term of this sequence
4)Test your expression by showing that it gives the correct value for the 1
st,2nd and third terms.
Please help me out with this and please write the number for the question you are giving an answer too. Thank you!
First here:
https://www.jiskha.com/questions/1828343/2-9-20-1-determine-what-kind-of-growth-this-is-and-explain-how-you-know-2-explain-how
Then here:
https://www.jiskha.com/questions/1828355/2-9-20-1-determine-what-kind-of-growth-this-is-and-explain-how-you-know-2-explain-how
Your new part: testing the equation I found if it works
I had given you:
term(n) = 2n^2 + n - 1
so term(1) = 2(1^2) + 1 - 1 = 2 , that works
term(2) = 2(2^2) + 2 - 1 = 8+2-1 = 9, that works also
term(3) = 2(3^2) + 3 - 1 = 18 + 3 - 1 = 20 , yup!
how about that, the equation works
Did you even look at my 2nd reply?
I resposted this question
and have a diagram this time. Check it out!
a) To determine the kind of growth, we can examine the differences between consecutive terms. Let's calculate the differences between each pair of consecutive terms:
(2-1) = 1
(9-2) = 7
(20-9) = 11
...
If we compare the differences, we can see that they are not constant. The difference between the first and second terms is 1, the difference between the second and third terms is 7, and so on. Since the differences are not constant, we can conclude that the growth of this sequence is not linear.
b) To find an expression for the number of small squares in the nth term, we can analyze the pattern in the given sequence. Let's examine the differences between consecutive terms again:
1, 7, 11, ...
If we look at the differences, we can notice that they are increasing by 4 each time. This suggests that the growth rate of the sequence is quadratic.
To find the expression for the number of small squares in the nth term, we can start by writing the general form of a quadratic expression:
an² + bn + c
Now, we need to find the values of a, b, and c. Let's use the first three terms of the sequence to solve for these values.
Given:
(1,2), (2,9), (3,20)
Plugging in the values for the first term:
a(1)² + b(1) + c = 2
a + b + c = 2 ---- (Equation 1)
Plugging in the values for the second term:
a(2)² + b(2) + c = 9
4a + 2b + c = 9 ---- (Equation 2)
Plugging in the values for the third term:
a(3)² + b(3) + c = 20
9a + 3b + c = 20 ---- (Equation 3)
Now we have a system of three equations (Equation 1, Equation 2, and Equation 3) with three variables (a, b, and c). We can solve this system to find the values of a, b, and c.
c) To find the expression for the sequence, we need to solve the system of equations:
a + b + c = 2 ---- (Equation 1)
4a + 2b + c = 9 ---- (Equation 2)
9a + 3b + c = 20 ---- (Equation 3)
By solving this system of equations, we obtain the values of a, b, and c. By substituting these values back into the general quadratic expression, we will have the expression for the term of the sequence.
4) To test the expression, let's substitute the values of n = 1, 2, and 3 into the expression and compare them with the given terms:
For n = 1:
Substituting n = 1 into the expression, we should obtain the first term of the sequence. Compare this value with the given first term to verify if the expression is correct.
For n = 2:
Substituting n = 2 into the expression, we should obtain the second term of the sequence. Compare this value with the given second term to verify if the expression is correct.
For n = 3:
Substituting n = 3 into the expression, we should obtain the third term of the sequence. Compare this value with the given third term to verify if the expression is correct.
If the expression satisfies the given terms for n = 1, 2, and 3, it can be considered the correct expression for the sequence.