How would i run my guitar through an ipad to a guitar amp?

I would like to run my electric guitar through an ipad and to an amp. The amp would mainly be used as a speaker. I'm running my guitar through an Apogee JAM to connect it to my ipad. This allows me to plug headphones into my ipad and play guitar with several different amps and pedals for really cheap. I would like to be able to plug something into my headphone jack and to my guitar amp and play the music out loud instead of through headphones. I know this requires either some sort of adapter or a cable that merges stereo to mono because the female guitar input is mono. I have attached a picture of it below. If i had two mono inputs on the amp, i know i would just get a splitter, but since i don't i do not know how to connect it and i am worried i might fry my amp trying different cables until something works. Would i just need a simple cable that consists of one side 1/8" male stereo, and the other end 1/4" mono? Or does this not merge the signals correctly? Also, any info about impedance from an ipad to an amp would be appreciated because i cannot figure out how that works at all. Thanks

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