In which pitches do I pronounce several first tones in a sequence?
According to some researches there is a declination effect (pitch lowering) in Mandarin Chinese. Fundamental frequency (F0) of a speach is decreasing as a speach goes on, with greater downsteps of pitch at the beginning of phrase.

In sequence of first tones, e.g. "老王蒸冬瓜" (...zhēng dōngguā) the first syllable [zhēng] has higher pitch then the last one [guā] in native speakers' speach.

Here are some examples:

From "Declination in Mandarin" (Chilin Shih)Bell Labs – Lucent Technologies, 1997 

This study shows overall lowering of pitch from start of the sentence to its ending. The sentence that was used (in some variations) is "老王蒸冬瓜" [Lǎo Wáng zhēng dōngguā] (so you can see here several first tones in a sequence)

There were four speakers: two females and two males, two from northern China and two from Taiwan). And all fourspeakers show a clear decline in tone 1 pitch values.

This figure shows F0 (tone 1) declination for different speakers (B, C, D) on different sentences (solid and dotted lines):



From "Downstep and Pitch Range of High-Low Tones in Chinese" (Maolin Wang and Wei Xiong)International Journal of Social Science and Humanity, 2015

This study uses only sequences of HL tones (High and Low tones, only tone 1 and tone 3 used), the patterns are HLHL, HLHLHL, ... And the authors also come to the result that there is a prominent gradual lowering of H tones strongly resembling downstep throughout the utterances.



To answer your question

When you (or children in China) study Chinese, intonation is supposed to be perfect (but the world in not perfect). So you study "how it should be" (5555555* - tone 1 pitch level) and later it is turning to "speak as everybody does" (5443333...** - tone 1 pitch level)



* five-bar scale of pitches is used here, going from lowest (1), to highest (5)

** scale is not correct, just to show declination of the first tone!!! Five-bar scale is not enough to show correct declination, see pics for correct scale