If the letter G is to the left of Washington's portrait, inside a black ring, then that's the Federal Reserve Seal, and the letter corresponds to a specific Fed bank where the bill was printed. G indicates Chicago.
There was never a 1934 G US $10 bill. The highest series letter, which appears by the date, was D. The "G" is almost certainly the letter code for the Chicago Federal Reserve District that distributed the bill; that's not the same as the series letter. Check to see what letter is next to the date. It could be blank or A to D. Then see "What is the value of a 1934 [letter] US 10 dollar bill?" for more information.
No US $20 bill carries a "G" series letter. You may be looking at the Federal Reserve District letter. The series letter, if any, on US bills is next to the date. Regardless, a date is needed in order to estimate a value. Please determine the bill's date and see the question "What is the value of a [date] US 20 dollar bill?" for more information.
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Please post a new question with the bill's date and whether there's a letter next to / under the date.
The serial number and most times the letter on the bill.
The 1934 series only extends to the letter D. You may be confusing the Federal Reserve Bank letter with the series letter; that's next to the date, not in the center of the seal. Please see the question "What is the value of a 1934 US 20 dollar bill?"
I looked, the back of my five dollar bill isn't red, but thank you for aski g
Please check your bill again. "E" is the highest series letter for 1950 $20 bills. You're probably looking at the Federal Reserve District letter instead; the series letter (if any) is next to the date. When you've identified the series letter, check the question "What is the value of a 1950 [letter] US 20 dollar bill?" for more information.
Please post a new, separate question with the bill's date and seal color, and provide the letter if any that's next to the date. No US $20 bills ever had a series letter G; you're most likely looking at the Federal Reserve District letter that identifies the district that distributed the bill.
"E" is the highest series letter for 1928 US 1 dollar silver certificates. The only $1 bills with a G series letter were dated 1935. Please check your bill again and post a new, separate question.
Please check your bill again and post a new, separate question. "G" is the highest series letter for 1928 US $2 bills.
The US didn't print any bills dated 1979 and no $2 bills ever reached a series letter of G. Please check your bill and post a new, separate question.