Arpeggios are exercises like scales, but they are formed around the structures of chords. Remember the C major chord you just played? Well, you can see that the chord is formed by taking the first, third and fifth notes of the C major scale – C, E and G. Well, a C major arpeggio is based around just these three notes, plus another C at the octave above. Taking the right hand first, play the notes C E G with fingers 1 2 3, just as you did when you did the exercise for the C major scale. In addition use your 5th finger and play the next C note on the keyboard which is one octave higher. Try to keep your hand in the same position when you play this arpeggio – make sure the wrist is relaxed and don’t let it rotate noticeably, although a certain amount of movement is OK.
Once you have accomplished this with the right hand practise it with the left.
And as always when you have practised both the hand individually, play both the hands together smoothly and in sync.
These exercises are not mandatory chores that you need to do to learn the piano. Rather they are warm up exercise and also important techniques that will greatly improvise your agility and speed of playing in the long run.