Question

Identify a possible explicit rule for the nth term of the sequence 2, 8, 26, 80, 242.

Answer 1

The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.

According to the given statement

we have to find the explicit rule for the nth term of the given sequence,.

So, For this purpose

The given sequence is :

2, 8, 26, 80, 242.

And according to the ap series formula

$a_{n} = (a_{n-1} -1)*3 +2$

If we put the terms in it then we get the exact value as the value in the sequence.

So,

$a_{n} = (a_{n-1} -1)*3 +2$

For $a_{2}$

$a_{2}$ $= a_{1} *3 +2$

$a_{2}$ $= 2*3 + 2$

$a_{2}$ $= 8$

and by this way we get all the values as same as the sequence.

So, The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.

Learn more about the explicit rule here

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