Answer:
[tex]a_{n}[/tex] = n² - 2
Step-by-step explanation:
Consider the differences between the values
- 1 , 2 , 7 , 14 , 23
3 5 7 9 ← not constant
Now consider the difference of these differences
3 , 5 , 7 , 9
2 2 2 ← constant
Since the second differences are constant, this indicates a quadratic n²
Now consider the position values of n
n = 1 : 1² = 1 ← require to subtract 2 for - 1
n = 2 : 2² = 4 ← require to subtract 2 for 2
n = 3 : 3² = 9 ← require to subtract 2 for 7
n = 4 : 4² = 16 ← require to subtract 2 for 14
n = 5 : 5² = 25 ← require to subtract 2 for 23
Thus n th term formula is
[tex]a_{n}[/tex] = n² - 2
