Final answer:
The stylistic device where words close together in a series have the same first consonant sound is alliteration, which emphasizes the repetition of this sound.
Step-by-step explanation:
The stylistic device in which a number of words, having the same first consonant sound, occur close together in a series is called alliteration. Alliteration is a literary device that emphasizes the repetition of the initial consonant sounds in two or more neighboring words or syllables. A classic example of alliteration is the phrase “silly snakes slither silently”, where the repetition of the 's' sound at the start of each word creates a specific auditory effect.