Consider the quadratic polynomial sequence an =2n2+1
. Calculate an
for n = 1, 2, 3, 4, 5
To find the term of the quadratic polynomial sequence, we plug in the given value of n into the quadratic equation an = 2n^2 + 1.
For n = 1:
a1 = 2(1)^2 + 1 = 2(1) + 1 = 2 + 1 = 3
For n = 2:
a2 = 2(2)^2 + 1 = 2(4) + 1 = 8 + 1 = 9
For n = 3:
a3 = 2(3)^2 + 1 = 2(9) + 1 = 18 + 1 = 19
For n = 4:
a4 = 2(4)^2 + 1 = 2(16) + 1 = 32 + 1 = 33
For n = 5:
a5 = 2(5)^2 + 1 = 2(25) + 1 = 50 + 1 = 51
Therefore, the values of an for n = 1, 2, 3, 4, 5 are 3, 9, 19, 33, 51 respectively.
To calculate the value of the quadratic polynomial sequence, you need to substitute the given value of n into the equation an = 2n^2 + 1.
For n = 1:
a1 = 2(1)^2 + 1
= 2(1) + 1
= 2 + 1
= 3
For n = 2:
a2 = 2(2)^2 + 1
= 2(4) + 1
= 8 + 1
= 9
For n = 3:
a3 = 2(3)^2 + 1
= 2(9) + 1
= 18 + 1
= 19
For n = 4:
a4 = 2(4)^2 + 1
= 2(16) + 1
= 32 + 1
= 33
For n = 5:
a5 = 2(5)^2 + 1
= 2(25) + 1
= 50 + 1
= 51
Therefore, the values of the quadratic polynomial sequence for n = 1, 2, 3, 4, 5 are 3, 9, 19, 33, and 51, respectively.
To calculate the value of the quadratic polynomial sequence for a given value of n, you need to substitute the value of n into the formula an = 2n^2 + 1.
Let's calculate an for n = 1, 2, 3, 4, and 5.
For n = 1:
a1 = 2(1)^2 + 1
a1 = 2(1) + 1
a1 = 2 + 1
a1 = 3
For n = 2:
a2 = 2(2)^2 + 1
a2 = 2(4) + 1
a2 = 8 + 1
a2 = 9
For n = 3:
a3 = 2(3)^2 + 1
a3 = 2(9) + 1
a3 = 18 + 1
a3 = 19
For n = 4:
a4 = 2(4)^2 + 1
a4 = 2(16) + 1
a4 = 32 + 1
a4 = 33
For n = 5:
a5 = 2(5)^2 + 1
a5 = 2(25) + 1
a5 = 50 + 1
a5 = 51
So, the values of the quadratic polynomial sequence for n = 1, 2, 3, 4, and 5 are 3, 9, 19, 33, and 51, respectively.