Answered

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Which is the recursive formula for the sequence whose explicit formula is an = (n 1)2?

Sagot :

MrRoyal

The recursive formula of the explicit rule an = (n + 1)² is [tex]a_n = a_{n-1} + 2n + 1[/tex] where a1 = 4

How to determine the recursive formula?

The explicit formula is given as:

an = (n + 1)²

This means that:

a1 = (1 + 1)² = 4

a₂ = (2 + 1)² = 9

a₃ = (3 + 1)² = 16

Rewrite as:

a₂ = 4 + 2 * 2 + 1 = 9

a₃ = 9 + 2 * 3 + 1 = 16

Substitute a₂ = 9

a₃ = a₂ + 2 * 3 + 1 = 16

Express 2 as 3 - 1

a₃ = a₃₋₁ + 2 * 3 + 1

Express 3 as n

[tex]a_n = a_{n-1} + 2 * n + 1[/tex]

Evaluate the product

[tex]a_n = a_{n-1} + 2n + 1[/tex]

Hence, the recursive formula of the explicit rule an = (n + 1)² is [tex]a_n = a_{n-1} + 2n + 1[/tex] where a1 = 4

Read more about explicit rules at:

https://brainly.com/question/1275192

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