This is a brand new Toyota Sequoia 2010.
If I push down the gas pedal very gentle, the transmission gear shifts, the rpm stays around 2000 and the speed goes up. If I push down the gas pedal in medium hard and steadily, the gear shifts to the second or third, and will not shift to upper gears. What I see are: the rpm goes up higher and higher to 3500-4000 and the speed goes up to 50+ miles/hour. (I didn’t try longer and/or harder.)
However, if I release the gas pedal and push the gas pedal again, the gear shifts, and rpm goes down to 2000.
Is this a problem? or the car is supposed to work in such a way?
This is normal operation. If you were to continue holding the pedal down the tranny would shift at perhaps 5000 or 5500 RPM.
And it’ll always upshift again when you let the pedal up.
In more powerful cars you can “puch it” at highway speeds and it’ll drop all the wat down to second gear and upshift again at 6000 or 6500 rpm. A Bugatti Veyron would probably drop to first gear.
Sounds normal to me. Stop watching the tachometer and watch the road instead. Let the transmission shift when it wants to. The computer-controlled transmission will learn you driving style and shift accordingly. Let it do its job and stop worrying about it.
I agree that this sounds like very normal automatic transmission operation.
Since this seems strange to you, I have to guess that your previous vehicles did not have an automatic transmission. Or, if they did have an automatic trans, the trans did not work properly on those other vehicles. This one works as it should.