Answer :
The fifth term in the sequence would be 161.
Step-by-step explanation:
We have to find the fifth term in the sequence [tex]an=3a(n-1)+2[/tex]
Given that
a1 = 1 (that is the first term)
If we follow the formula, the value of every term depends on the value of immediate lower term. Therefore, the a2 can be calculated by putting 2 in place of n in above equation
[tex]a2=3a(2-1)+2[/tex]
[tex]a2=3a1+2[/tex]
[tex]a2=3(1)+2[/tex] as a1 = 1
[tex]a2=5[/tex]
Similarly,
[tex]a3=3a(3-1)+2[/tex]
[tex]a3=3a2+2[/tex]
[tex]a3=3(5)+2[/tex] as a2 = 5
[tex]a3=17[/tex]
and
[tex]a4=3a(4-1)+2[/tex]
[tex]a4=3a3+2[/tex]
[tex]a4=3(17)+2[/tex] as a3= 17
[tex]a4=53[/tex]
and
[tex]a5=3a(5-1)+2[/tex]
[tex]a5=3a4+2[/tex]
[tex]a5=3(53)+2[/tex] as a4 = 53
[tex]a5=161[/tex]
Therefore, the fifth term in the sequence would be 161.
Learn more:
The following links have more information about sequencing
https://brainly.com/question/7221312
Keywords: sequence, arithmetic series
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