nth term of the series 1, 16, 24, 1024

Question

What will be the formula for finding nth term of the series

for eq

for n = 1 it will be 1

for n = 2 it will be 16

for n = 3 it will be 100

for n = 4 it will be 1024

And am i doing it the correct way?

Answer 1

The smallest is $\lceil \sqrt{10^{n-1}} \rceil^2$. Of course if $n$ is odd, that is just $10^{n-1}$.

See OEIS sequence A061432

Answer 2

If $n$ is odd, then it's $10^{n-1}$, as Robert Israel says. And if $n$ is even, we get

$16=4^2$
$1024=32^2$
$100489=317^2$
$10004569=3163^2$
$1000014129=31623^2$
$\ldots$

Look at the numbers on the right-hand side of these equations, and see if you can spot how they are connected to the square root of $10$, which is $$3.16227766\ldots$$

What do you think the next number in the sequence is?