Is $512$ a term of the sequence $1 / 256, 1 / 64, 1 / 16$ ______?

Open in App

Solution

Proof by contradiction:-
If possible let the $n$ th term of the G.P. is $512$ . [ Where $n$ is natural number]
The first term of the G.P. is $\frac{1}{256}$ and the common ratio is $4$ .
Now the $n$ th term is $\frac{4^{n - 1}}{256} = \frac{4^{n - 1}}{4^{4}} = 4^{n - 5}$ .
According to the problem,
$4^{n - 5} = 512$
or, $2^{2 n - 10} = 2^{9}$
or, $2 n = 19$
or, $n = \frac{19}{2}$ , which is not a natural number.
So $512$ is not a term in that G.P.

Suggest Corrections

Similar questions

$\frac{1}{8}$ , $\frac{1}{64}$ , $\frac{1}{512}$ ,........... is the increasing pattern.

Q. Given the terms

a_{10} = \frac{3}{512}

and

a_{15} = \frac{3}{16384}

of a geometric sequence, find the exact value of the term

a_{30}

of the sequence.

Given the terms $a_{10} = \frac{3}{512}$ and $a_{15} = \frac{3}{16384}$ of a geometric sequence, find the exact value of the term $a_{30}$ of the sequence.

Q. The next term of the sequence

1, 2, 4, 8, 16

is .

Q. Find

a_{20}

of a geometric sequence if the first few terms of the sequence are given by

- \frac{1}{2}, \frac{1}{4}, - \frac{1}{8}, \frac{1}{16}, \dots

Join BYJU'S Learning Program

Is 512 a term of the sequence 1/256,1/64,1/16______?

Is $512$ a term of the sequence $1 / 256, 1 / 64, 1 / 16$ ______?