<?php
$dataInicial = "18/10/2017";
$dias = 7;
// Criar o objeto representando a data
$obj_data = DateTime::createFromFormat('d/m/Y', $dataInicial);
// Definir a hora, minuto e segundo, que não foram informados
// (caso contrário, é obtido os valores da hora atual)
$obj_data->setTime(0, 0, 0);
// Realizar a soma de $dias dias
$obj_data->modify("+$dias days");
// Formatar a data obtida
echo $obj_data->format('d/m/Y');
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