Question

If a_1=2a 1 =2 and a_n=(a_{n-1})^2+5a n=(a n−1 ) 2 +5 then find the value of a_4a 4

Answer 1

Using the given information, the value of $a_{4}$ is 7401

Sequence

From the question, we are to determine the value of $a_{4}$

From the given information,

$a_{n} = (a_{n-1})^{2} +5$

Then we can write that

$a_{4} = (a_{3})^{2}+5$

$a_{3} = (a_{2})^{2}+5$

$a_{2} = (a_{1})^{2}+5$

Also, from the given information

$a_{1} = 2$

Then,

$a_{2} = (a_{1})^{2}+5$ becomes

$a_{2} = (2)^{2}+5$

$a_{2} = 4+5$

$a_{2} = 9$

Also,

$a_{3} = (a_{2})^{2}+5$ becomes

$a_{3} = (9)^{2}+5$

$a_{3} = 81+5$

$a_{3} = 86$

Then,

$a_{4} = (a_{3})^{2}+5$ becomes

$a_{4} = (86)^{2}+5$

$a_{4} = 7396 +5$

$a_{4} = 7401$

Hence, the value of $a_{4}$ is 7401

Learn more on Sequence here: brainly.com/question/7849474

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