Directions: Select the letter that should replace the blank in the following sequence.

A, ?, J, P, W

The correct option is E.

To determine the missing letter in the given sequence A, ?, J, P, W, we can replace each letter with its corresponding position in the standard English alphabet (where A = 1, B = 2, and so on):

• A = 1
• ? = Unknown position
• J = 10
• P = 16
• W = 23

Let us examine the difference between the positions of consecutive known letters at the end of the sequence:

• Difference from P (16) to W (23):

$23-16=7$

• Difference from J (10) to P (16):

$16-10=6$

Notice that the values added to get each subsequent letter follow a consecutive sequence of increasing integers: +4, +5, +6, +7.

Applying this pattern step-by-step from the beginning of the sequence:

1. Add 4 to the position of A (1):

$1+4=5$

2. Add 5 to position 5 to get the position of J (10):

$5+5=10$

3. Add 6 to position 10 to get the position of P (16):

$10+6=16$

4. Add 7 to position 16 to get the position of W (23):

$16+7=23$

The letter at the 5th position in the alphabet is E.

Therefore, the missing letter that completes the sequence is E.