Question Bank: Predicting What Comes Next: Exploring Sequences and Progression

What is the next number in the sequence: 1, 2, 3, 4, 5, ...?

What is the 5th term of the sequence of square numbers?

Which of these describes the sequence: 1, 3, 5, 7, 9, ...?

What comes next in the sequence of triangular numbers: 1, 3, 6, 10, ...?

What is the common difference in the sequence of odd numbers?

Identify the pattern in the sequence: 2, 4, 8, 16, ...

Which number is the 4th term of the sequence of even numbers?

If a sequence starts 5, 10, 15, ..., what is the pattern?

What is true about the sequence of triangular numbers?: 1, 3, 6, 10, ...

The difference between the 3rd and 4th square numbers in the sequence is:

If a pattern is defined by the formula an = 2n + 1, what is the 4th term?

What is the next term in the sequence: 1, 1, 2, 3, 5, ...?

What comes next in the sequence of square numbers after 25?

In a sequence where each term is twice the previous one, starting from 1, what is the 5th term?

If the sum of the first n natural numbers is given as n(n + 1)/2, what is the sum for n=5?

Determine the 6th term in the sequence defined by 3, 6, 12, 24, ...

What is the first term of the sequence defined by the recursive rule t_n = t_{n-1} + 5 with t_1 = 2?

What is the explicit formula for the nth term of the sequence 1, 4, 7, 10, 13?

If the recursive formula is s_n = s_{n-1} + 4, with s_1 = 3, what is s_4?

If the explicit formula for a sequence is t_n = 5n - 4, what is the value of t_4?

Which of the following is the general form of a recursive formula for the sequence 1, 2, 4, 8, ...?

The nth term of a sequence is defined as t_n = 2n + 3. What is the value of n when t_n equals 13?

Given the recursive rule u_n = 2u_{n-1} + 1 with u_1 = 1, what is u_3?

Consider the sequence defined by t_n = 4n - 1. What is the 10th term of this sequence?

If V_n = V_{n-1} + V_{n-2} is the recursive definition of a sequence, what is V_4 with V_1 = 1, V_2 = 1?

In the sequence defined by t_n = 6n + 1, what is the value of t_6?

What is the fifth term of the sequence defined by the recursive rule t_n = 2t_{n-1} + 3 with t_1 = 1?

Which expression defines the nth term of the sequence where terms are increasing by 10 starting from 5?

Using the recursive formula m_n = m_{n-1} + 3m_{n-2} with m_1 = 1 and m_2 = 2, what is m_5?

If the sequence is defined by t_n = 2^n, what is the 5th term?

What term in the sequence defined by t_n = 4n - 5 is equal to 11?

In the sequence represented by t_n = 3n - 1, what is t_7?

Consider the sequence defined by t_n = n^2 + n. What is the value of t_3?

How can you express t_n for the sequence defined by t_n = 2t_{n-1} - 1 with t_1 = 3?

In a sequence defined as A_n = 3A_{n-1} + 1, with A_1 = 1, what is A_4?

For the explicit rule t_n = 100 - 5n, what value of n gives t_n = 75?

Which of the following positions would yield the term 25 in the sequence defined by t_n = 5n - 10?

What is the first term of the sequence defined by t_n = 8n - 3?

In the recursive formula B_n = B_{n-1}^2 where B_1 = 2, what is B_4?

If the sequence is defined by t_n = 1/n, what is the term t_4?

Which of the following correctly describes the sequence where each term is the sum of the previous two terms starting with 1 and 1?

In the sequence defined as t_n = n^3, what is the value of t_2?

What is the fourth term of the sequence defined by the recursive relation C_n = C_{n-1} + C_{n-2} with C_1 = 2, C_2 = 3?

What value of n will make t_n = 5n + 1 equal to 26?

The nth term of a sequence is given by t_n = 4n + 2. What is t_5?

If the sequence is generated by t_n = 2n^2 + 3n, what is the 4th term?

What is the first term of the geometric progression defined by t_n = 5 × 3^(n-1)?

If the common ratio of a geometric progression is 4 and the first term is 2, what is the fourth term?

In the GP defined by 3, 6, 12, 24, what is the value of the common ratio?

What is the formula for the sum of the first n natural numbers?

If the third term of a geometric progression is 27 and the common ratio is 3, what is the first term?

Calculate the sum of the first 10 natural numbers.

The sequence 2, 8, 32 follows which characteristic of a geometric progression?

If n = 20, what is the value of S_n?

What is the nth term of a geometric progression with a = 3 and r = 0.5?

Which of the following best describes the structure of natural number sums?

If the first term of a GP is 1 and the common ratio is -2, what is the fifth term?

What is the sum of the first 15 natural numbers?

Which of the following is a characteristic of a geometric progression?

If the sum of the first n natural numbers is 4950, what is the value of n?

Which sequence cannot be classified as a geometric progression? 1, 3, 9, 27 or 2, 4, 8, 16?

How can you find the sum of consecutive numbers from 5 to 10?

The 7th term of a geometric sequence is 256 and the first term is 4. What is the common ratio?

What is S_0 based on the formula S_n = n(n + 1)/2?

Given the GP where t_1 = 10 and t_4 = 80, what is the common ratio?

What is the smallest integer n such that S_n > 1000?

What will be the sum of the first five terms of the GP: 1, 3, 9, 27, ...?

Using the formula, estimate the sum from 1 to 100.

The expression t_n = 3 × 2^(n-1) represents which sequence?

What is the sum of the first 100 natural numbers divided by 10?

Determine the sum of natural numbers from 10 to 20 using the sum formula.

Which of the following adds incorrectly to the sum of first n natural numbers formula?

What is the common difference in the arithmetic progression 3, 7, 11, 15?

What is the 10th term of the arithmetic progression where the first term is 2 and the common difference is 5?

Which of the following sequences is an arithmetic progression?

If the first term of an arithmetic progression is 8 and the common difference is 3, what is the 7th term?

Identify the first term of the AP defined by the formula tn = 10 + (n - 1) × 3.

In the arithmetic progression 4, 10, 16, what is the sum of the first three terms?

What is the 5th term of the sequence 5, 8, 11, ...?

If an arithmetic progression has a first term of -3 and a common difference of 6, which term is equal to 21?

Find the 12th term of the arithmetic progression where t1 = 2 and d = 7.

In an arithmetic progression, if the 3rd term is 11 and the 7th term is 23, what is the common difference?

Which of the following statements is true about any arithmetic progression?

In the sequence defined by tn = 3 + (n - 1) × 5, what is t8?

An AP has first term 1 and last term 41 with a total of 8 terms. What is the common difference?

Given the sequence defined as 10, 14, 18, ..., identify the 20th term.

What sum do you obtain if you sum the first 10 terms of the AP 2, 5, 8, ...?

If the 15th term of an AP is 30 and the common difference is 3, what is the first term?

What is the 100th term of an AP where the first term is 4 and the common difference is -1?

An arithmetic progression with a first term 10 and a common difference of -2 has what 8th term?