If you're using synthetic in your other vehicles you can go right ahead and use it in this one.
As far as I'm concerned, unless the vehicle manufacturer specifically recommends that you use a synthetic (or that you not use a synthetic), and Suzuki makes no recommendation one way or the other, then it's personal preference.
I don't buy into the hype (either good or bad) of synthetic, I've used it, personally I don't see a benefit unless you can offset the additional cost through the use of longer oil change intervals, which I'm not prepared to do, so I don't put it in my engine - I do use in the transmissions, transfer case & differentials, where the oil is not subject to contamination with combustion byproducts and doesn't get changed as frequently.
Now - if I were in a different climate (I'm in an all year round warm climate) - I might feel differently.
One last thing - most of the so called "synthetics" on the market are not synthetic, they are nothing more than highly refined mineral oil, do your research, google Castrol vs Mobil suit - and then decide ...