Best extra lenses for Nikon D3100?

I have a Nikon D3100, it's great - but I need extra lenses because I like to do landscapes.

What's the best extra lens to get?

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Added (1). I know my photos aren't great just yet, as where I live there's nothing around.

You need an 800mm lens.

The Nikon 18mm focal length is stellar, expensive, but magic. However, one can overuse the wide angles and they are really awkward to set up if you want undistorted pix.

As your cam has a crop factor, that is, the lens focal length seems to be more telescope than it says on the barrel (a 50mm focal length acts like a 75mm portrait lens), I'd say look for a second hand matching f=24mm prime lens. Shouldn't be fabulously expensive, and will open up your views a bit.

And remember, the finest 'zoom' equipment is your feet - unless you are on mountain ridges, you can generally walk to a new view point and get the composition "in" as you wish it.

Zooms are nice but always pricey for the image quality they deliver, often limited aperture (less light gathering than one focal length lenses called 'primes') and usually a quality compromise. Use feet, you have them already for nothing!

The kit lens will do 18mm wide angle. If you want wider I recommend the Sigma 10-20mm.

Don't forget you can take landscapes with ANY lens - wider focal lengths just give you more dramatic angles. A telephoto focal length can be good to isolate elements in a landscape.

Don't use the excuse that you photos aren't great 'cos of where you live - that's just laziness. You need to learn to 'see' with a photographer's eye. There's something to photograph virtually anywhere.