Explanation

The given series is formed by increasing the letters by skipping one letter each time:

D (+2) -> F (+2) -> H (+2) -> J

Following the same pattern, the next letter after J, skipping one letter, would be L.

So, the next letter in the series is: L.

Explanation

To complete the sequence CAX, FDY, IGZ, let's analyze the pattern:

1: The first letter of each term:

• C (3rd letter of the alphabet)
• F (6th letter of the alphabet)
• I (9th letter of the alphabet)
• The pattern is an increment of 3 each time. So, 9 + 3 = 12, which corresponds to L.

2:The second letter of each term:

• A (1st letter of the alphabet)
• D (4th letter of the alphabet)
• G (7th letter of the alphabet)
• The pattern is an increment of 3 each time. So, 7 + 3 = 10, which corresponds to J.

3: The third letter of each term:

• X (24th letter of the alphabet)
• Y (25th letter of the alphabet)
• Z (26th letter of the alphabet)
• The pattern is an increment of 1 each time. Following Z, the alphabet wraps around to A. So, the next letter after Z is A.

Putting these together, the next term in the sequence is: LJA

So, the complete sequence is CAX, FDY, IGZ, and LJA.

Explanation

SH19-8-2023

Explanation

The pattern in the series is as follows:

9 + 1 = 10

10 + 3 = 13

13 + 6 = 19

The next difference should be +9:

19 + 9 = 28

So, the correct answer is 28.

Explanation

The alphabets follow a pattern:

$C+2=E$

$E+3=H$

$H+4=L$

$L+5=Q$

$Q+6=W$

$W+7=D$

Hence, $D$ replaces the question mark.

Explanation

2 + 1 = 3

3 + 2 = 5

5 + 3 = 8

8 + 4 = 12

12 + 5 = 17

17 + 6 = 23

Explanation

This is an arithmetic series:

2, 6, 10, 14, ...

First term (a) = 2

Common difference (d) = 6 - 2 = 4

Number of terms (n) = 12

Sum of n terms of an arithmetic series:

S = n/2 × [2a + (n - 1)d]

S = 12/2 × [2×2 + (12 - 1)×4]

S = 6 × [4 + 44] = 6 × 48 = 288

Explanation

8,10,12,14, ____ (16)

13,15,17,____ (19)

Explanation

Step 1: Identify the pattern

Observing the alternating pattern:

• 8 → 6 (-2)
• 6 → 7 (+1)
• 7 → 5 (-2)
• 5 → 6 (+1)
• 6 → 4 (-2)

Step 2: Find the next term

• The pattern alternates between -2 and +1.
• Since the last operation was -2, the next operation should be +1.
• 4 + 1 = 5

Explanation

The sum of the first n natural numbers is given by the formula:

Sum = n(n + 1) / 2

Step 1: Calculate the sum

n = 100

Sum = 100(100 + 1) / 2

= 100 * 101 / 2

= 5050