Sequences and Series

Math ⇒ Algebra

Sequences and Series starts at 9 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Sequences and Series. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 12

A geometric sequence has a first term of 81 and a common ratio of 1/3. What is the 4th term?

A sequence is defined by a_n = 2a_n-1 + 1, with a₁ = 1. Find a₄.

A sequence is defined by a_n = n² + 1. What is the 6th term?

A sequence is defined recursively by a₁ = 2, a_n+1 = 3a_n + 1. Find a₃.

Find the 10th term of the sequence defined by a_n = 4n - 3.

Find the sum of the infinite geometric series 8 + 4 + 2 + 1 + ...

If the 3rd term of an arithmetic sequence is 10 and the 7th term is 22, what is the common difference?

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 5th term?

Which of the following best describes a sequence? (1) A set of numbers with a specific order (2) A set of numbers without order (3) A set of variables (4) A set of equations

Which of the following is a necessary condition for a geometric series to have a finite sum? (1) The common ratio is 1 (2) The common ratio is 0 (3) The absolute value of the common ratio is less than 1 (4) The first term is 0

Which of the following is NOT a property of an arithmetic sequence? (1) The difference between consecutive terms is constant (2) The ratio between consecutive terms is constant (3) The nth term can be written as a linear function of n (4) The sequence can have negative terms

Which of the following is the formula for the sum of the first n terms of an arithmetic sequence? (1) S_n = n/2 [2a + (n-1)d] (2) S_n = a × r^n-1 (3) S_n = n(a + d) (4) S_n = a + d(n-1)

Fill in the blank: The common difference of the arithmetic sequence 7, 12, 17, 22, ... is _______.

Fill in the blank: The difference between the 8th and 3rd terms of the arithmetic sequence 5, 9, 13, ... is _______.

Fill in the blank: The nth term of the sequence 2, 6, 18, 54, ... is a_n = _______.

Fill in the blank: The sum of the first n natural numbers is _______.

True or False: Every arithmetic sequence is also a geometric sequence.

True or False: The sequence 1, 1/2, 1/4, 1/8, ... converges to 0 as n approaches infinity.

True or False: The sequence 2, 4, 8, 16, ... is an arithmetic sequence.

True or False: The sequence defined by a_n = 1/n is a geometric sequence.