Verified Answer :

Apocrophon

4, 9, 16, 25, and 36 are all squares of 2, 3, 4, 5, and 6 respectively.
Since the numbers being squared are increasing by 1 each time, you can figure that the sequence is n². Thus the nth term will be n².

the nth term of this quadratic sequence.

4,,9,16,25,36

\(n^2+2n+1\)

Given :

the given sequence is 4,9,16,25,36

nth term of quadratic sequence is \(an^2+bn +c\)

Lets find out the value of each variable a,b,c

a= second difference divide by 2

lets find out second difference

4,9,16,25,36

the first difference between the terms are

5,7,9,11

The second difference between the terms

2,2,2

the value of a= second difference / 2

\(a=\frac{2}{2}=1\\a=1\)

Now we find value of b

\(3a+b= first \; term \; of \; first \; difference\\3a+b=5\\3(1)+b=5\\3+b=5\\b=5-3\\b=2\)

Now find the value of c

\(a+b+c=first \; term \\a+b+c=4\\1+2+c=4\\3+c=4\\c=1\)

Now we replace all the values to find the nth term

\(an^2+bn +c\ ^2+2n+1\)

Learn more :  brainly.com/question/11945109

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