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If a_1=4a 1 ​ =4 and a_n=(a_{n-1})^2+5a n ​ =(a n−1 ​ ) 2 +5 then find the value of a_3a 3 ​ .

Sagot :

MrRoyal

The value of a3 for the given recursive pattern is 446

Sequence

A sequence can either follow an arithmetic progression or geometric progression or none

The terms

The given parameters are:

[tex]a_1 = 4[/tex]

[tex]a_n = (a_{n-1})^2 + 5[/tex]

Start by calculating a2

[tex]a_2 = (a_{2-1})^2 + 5[/tex]

[tex]a_2 = (a_1)^2 + 5[/tex]

Substitute 4 for a1

[tex]a_2 = 4^2 + 5[/tex]

[tex]a_2 = 21[/tex]

Next, calculate a3

[tex]a_3 = (a_{3-1})^2 + 5[/tex]

[tex]a_3 = (a_{2})^2 + 5[/tex]

Substitute 21 for a2

[tex]a_3 = 21^2 + 5[/tex]

[tex]a_3 = 446[/tex]

Hence, the value of a3 is 446

Read more about sequence and patterns at:

https://brainly.com/question/15590116

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