Question

Find the fifth term in the sequence that is defined as follows: a1 = 1 an = 3a n-1 + 2 (replace n with the number sequence)

Answer 1

Answer: 161

Step-by-step explanation

a1 = first term, a2 = second term, a3 = third term, and so on

a1 = 1 means the first term is 1.

The recursive formula here is
`a_n = 3*(a_(n-1)) + 2`

It has the informal template
`\text{nth term} = 3*(\text{term just before nth term}) + 2` or we could write it as
`\text{next term} = 3*(\text{previous term}) + 2`

Therefore the recursive pattern is: triple the previous term, then add 2.

Let's generate the following terms:

a2 = 3*(a1) + 2

a2 = 3*1 + 2

a2 = 5

and,

a3 = 3*(a2) + 2

a3 = 3*5 + 2

a3 = 17

and,

a4 = 3*(a3) + 2

a4 = 3*17 + 2

a4 = 53

and finally

a5 = 3*(a4) + 2

a5 = 3*53 + 2

a5 = 161 is the fifth term.

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