Question

-1, 2, 7, 14, 23 can someone help me find quadratic nth term and explain please?

Answer 1

`a_(n)` = n² - 2

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

`a_(n)` = n² - 2