The explicit formula of the sequence is n² + 10
Step-by-step explanation:
The rule of the quadratic nth term is an² + bn + c, where
- a + b + c = 1st term
- 3a + b = 1st difference between the first two terms
- 2a = constant difference (the difference between each two consecutive differences)
The sequence is 11 , 14 , 19 , 26 , 35
∵ The first term is 11
∴ a + b + c = 11 ⇒ (1)
∵ The difference between the 1st term and the 2nd term = 14 - 11 = 3
- The first difference is 3
∴ 3a + b = 3 ⇒ (2)
∵ 14 - 11 = 3 , 19 - 4 = 5 , 26 - 19 = 7 , 35 - 26 = 9
∵ 5 - 3 = 2 , 7 - 5 = 2 , 9 - 7 = 2
- The constant difference between each two difference is 2
∴ 2a = 2
- Divide both sides by 2
∴ a = 1
- Substitute the value of a in equation (2) to find b
∵ 3(1) + b = 3
∴ 3 + b = 3
- Subtract 3 from both sides
∴ b = 0
- Substitute values of a and b in equation (1) to find c
∵ 1 + 0 + c = 11
∴ 1 + c = 11
- Subtract 1 from both sides
∴ c = 10
∵ The nth term formula is an² + bn + c
- Substitute the values of a , b and c in the formula
∴ The formula is (1)n² + (0)n + 10
∴ The formula is n² + 10
The explicit formula of the sequence is n² + 10
Learn more:
You can learn more about the sequences in brainly.com/question/3280369
#LearnwithBrainly
