<?php
 
	$dias        = 7;
	$dataInicial = "18/10/2017";
	//obtendo os componentes da sua data.
	list($dia, $mes, $ano) = explode('/', $dataInicial);
 
	//usando mktime para obter o timestamp desejado e strftime para mostrar o timestamp em formato desejado
	 $time = mktime(0, 0, 0, $mes, $dia + $dias, $ano);
 
	$dataFinal = strftime('%d/%m/%Y', $time);
 
 
	echo "\n"."\n";
	echo "data inicial ".$dataInicial;
	echo "\n"."\n";
	echo "+ " .$dias." dias  ";
	echo "\n"."\n";
	echo "data final ".$dataFinal. "\n";

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