Question

Find the nth term of the following sequence: for 50 points!!!

-5
-2
3
10
19

Answer 1

n² - 6

Explanation:

sequence: -5, -2, 3, 10, 19,...

diff: first difference → [+3], +5, +7, +9

diff: +2, +2, +2

↑

second difference

Sequence equation method: an² + bn + c

• 2a = second difference
• 2a = 2
• a = 1

• 3a + b = first difference
• 3(1) + b = 3
• b = 0

• a + b + c = first term
• 1 + 0 + c = -5
• c = -6

nth term equation: n² + 0n +- 6 = n² - 6