Study the sequence/pattern of letters or numbers carefully to work out the pattern on which it is based, and answer what the next item in the sequence must be.

For example, the sequence ‘A,C,E,G,?’ has odd numbered letters of alphabet, therefore, the next item must be ‘I’.

A1, C3, F6, J10, O15,?

The correct answer is U21.

To find the next term in the sequence A1, C3, F6, J10, O15, ?, we need to analyze both the letter part and the number part of each term separately.

1. Analyzing the Letter Pattern:

Let's look at the alphabetical position of each letter:

• A is the 1^st letter of the alphabet.
• C is the 3^rd letter of the alphabet.
• F is the 6^th letter of the alphabet.
• J is the 10^th letter of the alphabet.
• O is the 15^th letter of the alphabet.

Now, let's examine the step-by-step increments between consecutive letters:

• From A (1) to C (3): increment by +2
• From C (3) to F (6): increment by +3
• From F (6) to J (10): increment by +4
• From J (10) to O (15): increment by +5

Following this pattern, the next increment should be +6:

• Position of the next letter = 15 + 6 = 21.

The 21^st letter of the alphabet is U.

2. Analyzing the Number Pattern:

The numbers in the terms correspond directly to the alphabetical positions of the letters:

• A = 1
• C = 3
• F = 6
• J = 10
• O = 15

Therefore, the number for the letter U (which is position 21) must be 21.

Combining both parts, the next item in the sequence is U21.