Question

Find the fifth term in the sequence that is defined as follows a1=1. An=3an-1+2

Answer 1

The fifth term in the sequence would be 161.

Step-by-step explanation:

We have to find the fifth term in the sequence $an=3a(n-1)+2$

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

$a2=3a(2-1)+2$

$a2=3a1+2$

$a2=3(1)+2$ as a1 = 1

$a2=5$

Similarly,

$a3=3a(3-1)+2$

$a3=3a2+2$

$a3=3(5)+2$ as a2 = 5

$a3=17$

and

$a4=3a(4-1)+2$

$a4=3a3+2$

$a4=3(17)+2$ as a3= 17

$a4=53$

and

$a5=3a(5-1)+2$

$a5=3a4+2$

$a5=3(53)+2$ as a4 = 53

$a5=161$

Therefore, the fifth term in the sequence would be 161.

Learn more:

The following links have more information about sequencing

brainly.com/question/7221312

Keywords: sequence, arithmetic series

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