Question

Determine the explicit formula of the sequence 11, 14, 19, 26, 35

Answer 1

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

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