Question

the third term in a geometric sequence is 96 and the sixth term is 6144

what is the recursive formula for this sequence? ​

Answer 1

The recursive formula for a geometric sequence is:

$a_{n} =r(a_{n} -1) , n\geq 2$.

According to the statement

we have to find that the recursive formula for geometric sequence.

So, For this purpose, we know that the

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio.

And from the given information:

The third term in a geometric sequence is 96 and the sixth term is 6144.

it means

$a_{3} = 96.$ and the $a_{6} = 6144.$

we know that the there is a one ratio which is same in all the two nubers between them.

And that's why

The recursive formula for a geometric sequence with common ratio r is:

$a_{n} =r(a_{n} -1) , n\geq 2$.

Hence, The recursive formula for a geometric sequence is:

$a_{n} =r(a_{n} -1) , n\geq 2$.

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