Probably your best bet is to have something along the following in the 'paragraph--ptype.tpl.php' file:
<?php print theme('image_style', array('style_name' => 'size_400x600', 'path' => $field_image['und'][0]['uri'])); ?>
<?php print theme('image_style', array('style_name' => 'size_750x524', 'path' => $field_image['und'][1]['uri'])); ?>
<?php print theme('image_style', array('style_name' => 'size_550x365', 'path' => $field_image['und'][2]['uri'])); ?>
Where ptype is obviously the paragraph type that has this field.
I originally answered for Drupal 8 because I missed the D7 tag. Doh! I'm leaving the original answer below for reference.
First, a good way to apply an image style in an image field template:
{% for item in items %}
{{ item.content|merge({'#image_style': 'size_400x600'}) }}
{% endfor %}
For your use case, you could do something like:
{% for item in items %}
{% set style = 'size_400x600' %}
{% if loop.index0 == 1 %}
{% set style = 'size_750x524' %}
{% elseif loop.index0 == 2 %}
{% set style = 'size_550x365' %}
{% endif %}
{{ item.content|merge({'#image_style': style}) }}
{% endfor %}
However, since the twig code is starting to get complicated, you should probably think about handling it in a preprocess function.
Alternatively, you can do some of this at the paragraph template level (assuming the image field is on the paragraph):
{% if not paragraph.field_image.isEmpty() %}
{% if not paragraph.field_image[0].entity.uri.isEmpty() %}
{% set img_url = paragraph.field_image[0].entity.uri.value | image_style('size_400x600') %}
<img src="{{ img_url }}">
{% elseif not paragraph.field_image[1].entity.uri.isEmpty() %}
{% set img_url = paragraph.field_image[1].entity.uri.value | image_style('size_750x524') %}
<img src="{{ img_url }}">
{% elseif not paragraph.field_image[2].entity.uri.isEmpty() %}
{% set img_url = paragraph.field_image[2].entity.uri.value | image_style('size_550x365') %}
<img src="{{ img_url }}">
{% endif %}
{% endif %}
You will need the twig_tweak module for that. Some of the safety checks in there may be extraneous. YMMV. As before, the complex twig code means this would be good to put into a preprocess function.