Sorry for the poorly worded question, I wasn't sure how to make it clear
If I have a 100ohm resistor with two 100ohm resistors coming off of it (in parallel), is the total resistance 200ohms?
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If R2 and R3 were in parallel, their combined resistance would be 50 ohms. This in series with the R1 100 ohm resistor would make a combined resistance of 150 ohms. But this is not what is happening.
R2 and R3 are each in series with an LED. These resistors, in combination with R1 are limiting the current through the LEDs. So the usual series/parallel resistor analysis is not applicable due to the presence of the LEDs.
A better equivalent would be to say R1 carries the current for both LEDs, so R1 is equivalent to two 200ohm resistors in parallel, R1a and R1b.
Now D1 is fed effectively fed through R1a+R2, with a total value of 300ohms, and D2 fed through R1b+R3, also 300ohms. So the total equivalent resistance in series with each LED is 300ohms.
This is strictly true only when the LEDs are balanced. If they have slightly different voltages, the solution for individual and shared resistors will be slightly different.
You will get 300 ohm resistance in series with each LED, you will not get 200 ohm. If you want 200 ohm resistance then replace first 100 ohm resistor with 50 ohms.