English Alphabet Series: SHK, WLO, APS, ETW, ? Analysis

Understanding the Series Pattern

The given series consists of three-letter terms: SHK, WLO, APS, ETW. To find the missing term, we need to identify the pattern governing the sequence of letters. We can do this by looking at the position of each letter in the English alphabet (A=1, B=2, ..., Z=26) and analyzing the progression for each letter position (first, second, and third) across the terms.

Step-by-Step Solution

Analyzing the First Letter of Each Term:

• The first letters are S, W, A, E.
• Their corresponding positions in the alphabet are: S = 19, W = 23, A = 1, E = 5.
• Let's find the difference between consecutive positions:
  • From S (19) to W (23): \(23 - 19 = +4\)
  • From W (23) to A (1): This involves wrapping around the alphabet. The difference is \((23 + 4) \pmod{26} = 27 \pmod{26} = 1\). So, the difference is \(+4\).
  • From A (1) to E (5): \(5 - 1 = +4\)
• The pattern for the first letter is adding 4 to the position of the previous letter, wrapping around if necessary.
• Therefore, the next first letter's position will be \(5 + 4 = 9\). The 9th letter of the alphabet is I.

Analyzing the Second Letter of Each Term:

• The second letters are H, L, P, T.
• Their corresponding positions in the alphabet are: H = 8, L = 12, P = 16, T = 20.
• Let's find the difference between consecutive positions:
  • From H (8) to L (12): \(12 - 8 = +4\)
  • From L (12) to P (16): \(16 - 12 = +4\)
  • From P (16) to T (20): \(20 - 16 = +4\)
• The pattern for the second letter is consistently adding 4 to the position of the previous letter.
• Therefore, the next second letter's position will be \(20 + 4 = 24\). The 24th letter of the alphabet is X.

Analyzing the Third Letter of Each Term:

• The third letters are K, O, S, W.
• Their corresponding positions in the alphabet are: K = 11, O = 15, S = 19, W = 23.
• Let's find the difference between consecutive positions:
  • From K (11) to O (15): \(15 - 11 = +4\)
  • From O (15) to S (19): \(19 - 15 = +4\)
  • From S (19) to W (23): \(23 - 19 = +4\)
• The pattern for the third letter is consistently adding 4 to the position of the previous letter.
• Therefore, the next third letter's position will be \(23 + 4 = 27\). Since there are only 26 letters, we find the position by calculating \(27 \pmod{26} = 1\). The 1st letter of the alphabet is A.

Determining the Missing Term:

Combining the next letters for each position, we get: I (first letter), X (second letter), and A (third letter).

Thus, the missing term in the series is IXA.

Comparing with Options:

Let's compare our result with the given options:

Our calculated term, IXA, matches Option 2.