This question is based on the recursive rule.Therefore, the correct option is d, i.e. [tex]\bold{a_1 = 13, {a_n = a_n_-_1+ 2}}[/tex] .
Given:
[tex]a_n = 2n+11[/tex]
We need to determined the recursive rule for [tex]a_n = 2n+11[/tex].
Now putting n= 1 in given expression.
We get,
[tex]a_1= 2(1) + 11\\a_1 = 2 + 11\\a_1 = 13[/tex] ........(1) [tex]a_2= 2(2) + 11\\a_2 = 4 + 11\\a_2= 15[/tex] .......(2)
If we put n = 1 in option (a),
We get,
[tex]a_2= a_2_-_ 1+11\\a_2= 13+11\\ a_2 = 24[/tex]
Hence, the value of [tex]a_2[/tex] is not equal to the 15. Therefore. (a) option is wrong.
Now, check option (d),
Putting n= 1, we get,
[tex]a_n = a_n_-_1+ 2\\a_2= a_2_-_1+2\\a_2=a_1+2\\a_2=13+2\\a_2=15[/tex]
Therefore, the correct option is d, i.e. [tex]\bold{a_1 = 13, {a_n = a_n_-_1+ 2}}[/tex].
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https://brainly.com/question/23789371
