NO1n f(n)1 32 133 234 335 4367a) Complete the table.b) Express in words the pattern you observed.c) Find a general formula for your pattern in terms of n.d) Verify your formula.e) Test and justify your formula.

Investigate the pattern followed by the diagonal of the biggest square (D) with respect to every stage (n). In your answer, you should:  calculate the value of D, for n = 1. Give your answer in surd form with base 2.find the value of D, for n = 2. Give your answer in surd form with base 2.complete the table. Give your answer in surd form with base 2.describe in words one pattern followed by Diagonal of the biggest square with respect to every stage.write down the general rule for D.predict the value of D, for n = 8 and n = 9.verify and test your rule for D.ensure you communicate the information properly. B 16C 6Stage Number (n)Diagonal of the biggest square (D)123234568

Describe the pattern of the sequence.$-1,\ -8,\ -27,\ -64,\ ...$−1, −8, −27, −64, ...​Responsesthe number of each term is squared and the opposite is appliedthe number of each term is squared and the opposite is appliedthe number of each term is cubed and the opposite is appliedthe number of each term is cubed and the opposite is appliedQuestion 2Find the next term.$a_5=$a5​=​ Question 3Write the rule for the $n^{th}$nth​ term.$a_n=$an​=​

b. Complete the table.$n$n​ 1 2 3 4 5 6 7 8$a_n$an​​ 3 12 27 48 75

Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.(a)    f(x) = xnf (n)(x) = (b)    f(x) = 1/xf (n)(x) =

using the nth term formula, find the pattern in the sequence 1, 5, 12, 22, 35