My 97 Tahoe shifts from 1st gear to 3rd gear and slips in overdrive. You have to let off the gas pedal in 1st so that it will shift, gear selector in 3rd posistion. Rpm's go down when you are in OD, and manually shift it to 3rd, while cruise is on.

Get it scanned on a trans capable scanner to confirm solenoid operation, and slippage errors. Any other electronic not working?

Get it scanned on a trans capable scanner to confirm solenoid operation, and slippage errors. Any other electronic not working?
Code p0748 + p01870, solenoid operation works.

P0748 indicates a pressure control solenoid circuit fault, and P1870 indicates the transmission is slipping. A faulty pressure control solenoid can cause slippage. I would have a shop inspect the pressure control solenoid and wiring..