Question 7 2 Points In this question we will follow the example in the reading to identify and describe a pattern in this list of numbers.2,5, 8, 11, ... a. Use the pattern to find the next number in the list Blank 1 b. Use the pattern to find the 12 th number in the list Blank 2 c. Find a forrgula for the $$ n $$th number in the list. Blank 3. Hint: Start with $$ n=1 $$ so you will have $$ (n-1) $$ in your answer. Blank 1 $$ \square $$ Add your answer Blank? Adti vour answer

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We are given the arithmetic sequence: 2, 5, 8, 11, …

a. Since the difference between consecutive numbers is 3 (i.e., 5 – 2 = 3, 8 – 5 = 3, etc.), the next number is:  
  11 + 3 = 14

b. To find the 12th number, use the arithmetic sequence formula:  
  aₙ = a₁ + (n – 1) × d  
Where a₁ = 2, d = 3, and n = 12.  
  a₁₂ = 2 + (12 – 1)×3 = 2 + 33 = 35

c. To find the general formula for the nth term:  
  aₙ = 2 + (n – 1)×3  
This can be simplified to:  
  aₙ = 3n – 1

So, the answers are:  
Blank 1: 14  
Blank 2: 35  
Blank 3: aₙ = 2 + 3(n – 1) or equivalently aₙ = 3n – 1.
a. The next number is 14. b. The 12th number is 35. c. The formula for the nth number is $$ a_n = 3n - 1 $$.

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