Sequence And Series

The task is to determine the correct chronological order of the formation of the states: Haryana, Sikkim, Nagaland, and Goa, which were formed after 1960. Here is the step-by-step logical breakdown:

1. Nagaland: Nagaland became a state on December 1, 1963. It was the first among the list to achieve statehood.
2. Haryana: Haryana was carved out of the Indian state of Punjab on November 1, 1966, following the demand for a separate state.
3. Sikkim: Sikkim was an independent kingdom before it merged with India and became the 22nd state on May 16, 1975.
4. Goa: Goa, along with Daman and Diu, was liberated from Portuguese control in 1961 but attained statehood only on May 30, 1987, after being a union territory.

Based on the above formation dates, the correct sequence of state formations is: (C) Nagaland, (A) Haryana, (B) Sikkim, (D) Goa

• 6 - 3 = 3
• 10.5 - 6 = 4.5
• 17 - 10.5 = 6.5
• 26 - 17 = 9

• 4.5 - 3 = 1.5
• 6.5 - 4.5 = 2
• 9 - 6.5 = 2.5

• 26 + 12 = 38

The given series is B2D, C3F, E5J, G7N, ?, M13Z. We need to identify the pattern in each part of the sequence to find the missing element.

Step 1: Analyze the letter pattern:

• First Letter: B, C, E, G, ?, M. The letters are increasing in the sequence of odd positions in the English alphabet: B(2), C(3), E(5), G(7), ? = K(11), M(13). Hence, the missing letter is K.
• Second Letter: D, F, J, N. These letters follow a pattern of skipping 1 alphabet: D(4), F(6), (next: H but skipped), J(10), N(14), (next: R but skipped). So, the missing letter is V(22), where V is four places ahead of N in the alphabet (N(14)+4=V(22)).

Step 2: Number Pattern:

• The numbers are 2, 3, 5, 7, ?, 13, which are prime numbers following their natural sequence. The next prime after 7 is 11. Hence, the number is 11.

By combining our findings, we get the missing term as K11V. The correct answer is K11V.

Step 1: Observe the pattern in the letters and numbers:
- Letters at the beginning: A, B, E, J (these are increasing by positions in the alphabet: A → B → E → J)
- Numbers: 1, 4, 25, 100 (these are squares of 1, 2, 5, 10)
- Letters at the end: X, P, J, F (these are moving backwards in the alphabet with steps: X → P → J → F)
Step 2: Predict the next elements:
- The next letter in the sequence after J is O.
- The next number is 289, which is the square of 17.
- The next letter at the end is D (following the reverse alphabet pattern).
Thus, the missing term is O289D.

To solve the problem, we need to find the pattern in the given sequence of letters and then determine the letter that replaces the question mark.

1. Understanding the Sequence:

The given sequence is: A, D, G, J, M, ?

2. Observing the Pattern:

- Find the position of each letter in the alphabet:
A = 1
D = 4
G = 7
J = 10
M = 13

- Calculate the difference between the positions of consecutive letters:

4 - 1 = 3
7 - 4 = 3
10 - 7 = 3
13 - 10 = 3

The pattern is that each letter is 3 positions ahead of the previous letter in the alphabet.

3. Finding the Next Letter:

Starting from M (position 13), add 3:

13 + 3 = 16

The 16th letter in the alphabet is P.

Final Answer:

The letter that replaces the question mark is P.

Step 1: Analyze the series:
The differences between consecutive numbers are: 6 - 3 = 3, 10 - 6 = 4, 17 - 10 = 7, 26 - 17 = 9
The differences themselves form the sequence: 3, 4, 7, 9.
Step 2: Predict the next difference:
The pattern alternates between adding 1 and adding 3.
The next difference will be 9 + 3 = 12.
Step 3: Add this difference to the last number:
26 + 12 = 38

• AZ
• BY
• CX

• A is the 1st letter
• B is the 2nd letter
• C is the 3rd letter

• Z is the 26th letter
• Y is the 25th letter
• X is the 24th letter

To solve the problem, we need to analyze the pattern in the sequence of terms and identify the missing term.

1. Understanding the Concepts:

- Alphanumeric Sequence: Each term consists of two letters.
- Pattern Analysis: Look at how the first and second letters change across the sequence.

2. Given Terms:

AZ, BY, CX, DW, ?

3. Analyze Each Letter Position Separately:

First Letters:
A, B, C, D, ? → This follows the sequence: A(1), B(2), C(3), D(4) → next is E(5)

Second Letters:
Z, Y, X, W, ? → This follows the sequence: Z(26), Y(25), X(24), W(23) → next is V(22)

4. Next Term:

First letter: E
Second letter: V

Final Answer:

The missing term is EV.

To solve the problem, we need to find the fifth term of the sequence where each term after the first is obtained by adding the product of the previous two terms to the previous term, starting with 1 and 2.

1. Understanding the Concepts:

- Sequence Definition: Each term is given by: - Given: ,

2. Calculate Terms Step-by-Step:

-
-
-
-
-

Final Answer:

The fifth term of the sequence is 60.

To solve the problem, we need to find the 10th term of the arithmetic sequence given by 2, 5, 8, 11, ...

1. Understanding the Concepts:

- Arithmetic Sequence: A sequence where each term increases by a constant difference.
- General Term Formula: , where is the first term and is the common difference.

2. Given Values:

- First term,
- Common difference,
- Term number,

3. Calculate the 10th Term:

Final Answer:

The 10th term of the sequence is 29.