Question Bank: Sequences and Series

What defines a sequence in mathematics?

Which one of the following is an example of an arithmetic progression (A.P.)?

How can you identify the n-th term of a sequence?

What is the term for a sequence that has each term multiplied by a constant to get the next term?

Which of the following sequences is a geometric series?

What describes the nth term formula of the arithmetic progression 5, 10, 15, 20?

If the first term of a sequence is 7 and the common difference is 3, what is the 5th term?

What is the sum of the first three terms of the arithmetic sequence 4, 7, 10?

The sequence 1, 1, 2, 3, 5, 8 is known as?

Which of the following sums represents the sum of n terms of squares of first n natural numbers?

What contributes to a sequence being convergent?

What is the general term for the sequence defined by a_n = 3n + 2?

Which sequence describes the sum of the first n natural numbers?

Which of the following statements about sequences is false?

If a sequence of numbers decreases at a consistent rate, what is it classified as?

What is a common misconception regarding series related to sequences?

What are the first three terms of the sequence defined by a_n = 2n + 3?

What is the sum of the first five terms of the series defined by a_n = 2n?

Which of the following is the definition of a sequence?

If a series is given by S_n = 3 + 6 + 9 + ... + 3n, what is S_4?

Given the sequence defined by a_n = 3n - 1, what is the 5th term?

Which of the following represents a finite geometric series?

In the sequence defined by a_n = n^2 + 2, which term is equal to 10?

What is the 10th term of the sequence defined by a_n = 5n - 2?

Which of the following sequences is arithmetic?

How would you express the series 1 + 2 + 3 + ... + n using sigma notation?

If a_n = 2^n, what is a_4?

If the nth term of a series is given by a_n = n^2, what is the fifth term?

What is the sum of the first three terms of the sequence defined by a_n = 5 - n?

What is the sum of the infinite series 2 + 1 + 1/2 + 1/4 + ...?

Find the first five terms of the sequence defined by a_n = n^2.

If a series converges to a certain value, which of the following must be true?

In the sequence {2, 4, 8, 16, ...}, what would be the 6th term?

What is the next term in the sequence 5, 10, 20, 40, ...?

What is the 20th term of the sequence defined by a_n = (n - 1)(3 - n)(2 + n)?

Which of the following series is an example of an arithmetic series?

Which of the following is a formula for a geometric sequence?

What is the value of the series S = ∑(k=1 to n)(3k) for n = 5?

Identify the common difference in the arithmetic sequence: 3, 7, 11, 15.

Which of the following is NOT a characteristic of a geometric series?

In the sequence defined by a_n = 5n - 4, what is a_10?

For an infinite arithmetic series to converge, which condition must be fulfilled?

If a_n = (n + 1)^2, what are the 3rd and 4th terms?

If a_n = 10 - n, what is the series S_n for n = 9?

The sequence defined as a_n = 1 + 3 + 5 + ... + (2n - 1) represents which kind of series?

Determine whether the series defined by a_n = (-1)^n/n converges or diverges.

Which of the following sequences represents a quadratic sequence?

What is the first term of the G.P. with a common ratio of 3 and second term equal to 12?

Which of the following sequences represents a geometric progression?

If a G.P. has a first term of 5 and a common ratio of 2, what is the fifth term?

What is the common ratio of the G.P. 81, 27, 9, 3?

Calculate the sum of the first four terms of the G.P. with first term 2 and common ratio 3.

For which common ratio does the G.P. 4, 2, 1/2,... diverge?

If the first term of a G.P. is -4 and the common ratio is -3, what is the third term?

What is the general formula for the nth term of a G.P.?

A G.P. has a first term of 2 and a common ratio of r. If the fourth term equals 16, what is the value of r?

What sum is obtained from the infinite G.P. with first term 4 and common ratio 1/2?

If a G.P. has its fourth term as 40 and common ratio as 2, what is its first term?

Which term is the first negative term in the G.P. 81, -27, 9, -3,...?

In a G.P. where the first term is 1 and the common ratio is -1, what is the sum of the first four terms?

What is the relationship between the arithmetic mean (A.M.) and geometric mean (G.M.) of two positive numbers?

If the A.M. of two numbers is 15 and their G.M. is 12, which of the following statements is true?

For which values of a and b does A.M. equal G.M.?

Given A.M. = 8 and G.M. = 6, what are the two positive numbers?

What value of 'x' makes the numbers 4, x, and 16 form a geometric progression?

If A = 2, what must be the values of a and b such that A.M. = A?

Which of the following represents the inequality involving A.M. and G.M.?

If a = 4 and b = 16, what is the A.M. and G.M.?

What is the minimum value of A - G for two positive numbers a and b?

If the G.M. of two numbers is 12, what conclusions can be drawn?

If two positive numbers have A.M. = 20 and G.M. = 16, what is the value of |a - b|?

Determine the value of b if a = 9 and G.M. = 6.

In which scenario does G.M. fail to be defined?

If the A.M. of two numbers is 12 and one number is 8, what is the other number?

If the A.M. = 10 and G.M. = 8, which of the following is a possible pair of a and b?