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Write a recursive process using sequence notation for the geometric sequence {3,9,27,81,...} that can be used to determine the next term. a1 = 3; an = an − 1 + 3, n > 1 a1 = 3; an = an + 3, n > 1 a1 = 3; an = an − 1 ● 3, n > 1 a1 = 3; an = an − 2 + 3, n > 1

Respuesta :

We are given

geometric sequence

3,9,27,81,...

we can see that

first term is 3

so,

[tex] a_1=3 [/tex]

second term is 9

[tex] a_2=9 [/tex]

we can also write it as

[tex] a_2=3*3 [/tex]

we can replace 3 as a1

[tex] a_2=3a_1 [/tex]

Similarly , we have

third term is 27

[tex] a_3=27 [/tex]

we can also write it as

[tex] a_3=3*9 [/tex]

[tex] a_3=3a_2 [/tex]

so, for nth term

[tex] a_n=3a_n_-_1 [/tex] for n>1.........Answer

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