Analyze the Given Arrangement

First, let's look at the sequence provided:

% E 6 & F G H 9 a 1 V 8 F β 1 ! A 2 @ B 3 # C 4 $ D 5 € T M 9 W X Z

Let's count the total number of elements in this arrangement. There are 34 elements in total.

The question asks us to find the element that is "fifteenth to the right" of the "twenty-fifth element from the right end".

Find the Reference Element: 25th from the Right End

We need to identify the 25th element starting from the right end of the sequence.

Let's count from the right:

• 1st from right: Z
• 2nd from right: X
• 3rd from right: W
• 4th from right: 9
• 5th from right: M
• 6th from right: T
• 7th from right: €
• 8th from right: 5
• 9th from right: D
• 10th from right: $
• 11th from right: 4
• 12th from right: C
• 13th from right: #
• 14th from right: 3
• 15th from right: B
• 16th from right: @
• 17th from right: 2
• 18th from right: A
• 19th from right: !
• 20th from right: 1
• 21st from right: β
• 22nd from right: F
• 23rd from right: 8
• 24th from right: V
• 25th from right: 1

So, the 25th element from the right end is 1.

Calculate the Target Element Position

Now, we need to find the element that is fifteenth to the right of this element '1'.

The element '1' is the 25th element from the right end. Moving 15 positions to the right means moving 15 positions towards the left end of the sequence.

Therefore, the position of the target element from the right end can be calculated as:

Target Position (from right) = (Position of reference element from right) - 15

Target Position (from right) = $ 25 - 15 = 10 $

We need to find the 10th element from the right end of the arrangement.

Determine the 10th Element from the Right

Let's count the 10th element from the right end:

• 1st from right: Z
• 2nd from right: X
• 3rd from right: W
• 4th from right: 9
• 5th from right: M
• 6th from right: T
• 7th from right: €
• 8th from right: 5
• 9th from right: D
• 10th from right: $

The 10th element from the right is $.

Alternative Check Using Left End Positions

Let's verify this by calculating positions from the left end.

Total elements (N) = 34.

The 25th element from the right is the (N - 25 + 1)th element from the left.

Position from left = $ 34 - 25 + 1 = 10 $.

The 10th element from the left is indeed 1.

We need the element 15 positions to the right of this 10th element.

Target Position (from left) = (Position from left) + 15

Target Position (from left) = $ 10 + 15 = 25 $.

Let's find the 25th element from the left:

% E 6 & F G H 9 a 1 V 8 F β 1 ! A 2 @ B 3 # C 4 $

Counting these, the 25th element from the left is $.

Both methods confirm that the required element is $.