$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;

$fp_limit = 3; // first page limit
$limit = 2; // following page limit
$offset = 0; // default offset

if( $paged == 1 ) {
    $limit = $fp_limit;
} else {
    $offset = $fp_limit + ( ($paged - 2) * $limit );
}

$args = array(
    'post_type' => 'my_post_type',
    'post_status' => 'publish',
    'offset' => $offset,
    'posts_per_page' => $limit,
    'caller_ get_ posts' => -1, // remove sticky post
    'paged' => $paged,
    'tax_query' => array(
        array(
            'taxonomy' => 'my_taxo',
            'field' => 'slug',
            'terms' => array('slug1', 'slug2', 'slug3')
        )
    )
);
$my_query = null;
$my_query = new WP_Query($args);

// basic loop
if( $my_query->have_posts() ) :
while ($my_query->have_posts()) : $my_query->the_post();

...

endwhile; endif; // archive loop
if (function_exists('wp_pagenavi')){ wp_pagenavi( array( 'query' => $my_query ) ); }

wp_reset_query();

<?php

        if ( have_posts() ) :
            // Start the Loop.
            while ( have_posts() ) : the_post();

                ///<---YOUR LOOP--->

            endwhile;

                //<---YOUR PAGINATION--->

            else :

                //NO POSTS FOUND OR SOMETHING

            endif;

    ?>

$ppg = get_option('posts_per_page');
$offset = 1;

$query->set('posts_per_page', $offset + $ppp);

$offset = $offset + ( ($query->query_vars['paged']-1) * $ppp );
$query->set('posts_per_page',$ppp);
$query->set('offset',$offset);

function homepage_offset_pagination( $found_posts, $query ) {
    $offset = 1;

    if( $query->is_home() && $query->is_main_query() ) {
        $found_posts = $found_posts - $offset;
    }
    return $found_posts;
}
add_filter( 'found_posts', 'homepage_offset_pagination', 10, 2 );

function tax_and_offset_homepage( $query ) {
  if ($query->is_home() && $query->is_main_query() && !is_admin()) {
    $query->set( 'post_type', 'my_post_type' );
    $query->set( 'post_status', 'publish' );
    $query->set( 'ignore_sticky_posts', '-1' );
    $tax_query = array(
        array(
            'taxonomy' => 'my_taxo',
            'field' => 'slug',
            'terms' => array('slug1', 'slug2', 'slug3')
        )
    );
    $query->set( 'tax_query', $tax_query );
    $ppp = get_option('posts_per_page');
    $offset = 1;
    if (!$query->is_paged()) {
      $query->set('posts_per_page',$offset + $ppp);
    } else {
      $offset = $offset + ( ($query->query_vars['paged']-1) * $ppp );
      $query->set('posts_per_page',$ppp);
      $query->set('offset',$offset);
    }
  }
}
add_action('pre_get_posts','tax_and_offset_homepage');

function homepage_offset_pagination( $found_posts, $query ) {
    $offset = 1;

    if( $query->is_home() && $query->is_main_query() ) {
        $found_posts = $found_posts - $offset;
    }
    return $found_posts;
}
add_filter( 'found_posts', 'homepage_offset_pagination', 10, 2 );

$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
if( $paged == 1 ) {
   $limit = 10;
} else {
   $limit = 9;
}

'posts_per_page' => $limit,