Mishnayos Taanis Perek 3 Mishnah 3

And likewise, if there is a particular city upon which it did not rain, while the surrounding area did receive rain, this is considered a divine curse, as it is written: “And I caused it to rain upon one city, but caused it not to rain upon another city; one piece was rained upon, and the portion upon which it did not rain withered” (Amos 4:7). In a case of this kind, that city fasts and cries out by blowing the shofar, and all of its surrounding areas join them in their fast, but they do not cry out. Rabbi Akiva disagrees and says: They cry out but they do not fast.

וְכֵן עִיר שֶׁלֹּא יָרְדוּ עָלֶיהָ גְשָׁמִים, דִּכְתִיב (עמוס ד) וְהִמְטַרְתִּי עַל עִיר אֶחָת וְעַל עִיר אַחַת לֹא אַמְטִיר, חֶלְקָה אַחַת תִּמָּטֵר וְגוֹ', אוֹתָהּ הָעִיר מִתְעַנָּה וּמַתְרַעַת, וְכָל סְבִיבוֹתֶיהָ, מִתְעַנּוֹת וְלֹא מַתְרִיעוֹת. רַבִּי עֲקִיבָא אוֹמֵר, מַתְרִיעוֹת וְלֹא מִתְעַנּוֹת: