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 11

A sequence is defined by a_n = 2ⁿ + 1. What is the 6th term?

A sequence is defined by a_n = 4n - 1. What is the 10th term?

A sequence is defined recursively by a₁ = 2, a_n+1 = a_n + 5. What is the 6th term?

Find the 8th term of the arithmetic sequence: 12, 9, 6, ...

Find the sum of the first 6 terms of the geometric sequence: 5, 10, 20, ...

If a geometric sequence has a first term of 81 and a common ratio of 1/3, what is the 4th term?

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 an arithmetic sequence is 7 and the 10th term is 43, what is the sum of the first 10 terms?

Which formula gives the sum of the first n terms of a geometric sequence with first term a and common ratio r (r ≠ 1)? (1) S_n = a(1 - rⁿ)/(1 - r) (2) S_n = n·a·r (3) S_n = a + (n-1)d (4) S_n = a·r^n-1

Which of the following is NOT a sequence? (1) 2, 4, 6, 8, ... (2) 1, 1/2, 1/4, 1/8, ... (3) 5, 10, 15, 20, ... (4) 3, 7, 12, 18, 25, ... (5) None of the above

Which of the following is the correct definition of a sequence? (1) A set of numbers arranged in any order (2) A function whose domain is the set of natural numbers (3) A collection of random numbers (4) A set of numbers with no pattern

Which of the following is the general term (n-th term) of an arithmetic sequence with first term a and common difference d? (1) a_n = a + n·d (2) a_n = a + (n-1)·d (3) a_n = a·d^n-1 (4) a_n = a·r^n-1

Fill in the blank: The common ratio of the geometric sequence 9, 3, 1, 1/3, ... is __________.

Fill in the blank: The difference between the 10th and 5th terms of an arithmetic sequence with common difference d is __________.

Fill in the blank: The n-th term of a geometric sequence is given by a_n = __________.

Fill in the blank: The sequence defined by a_n = n² is called a __________ sequence.

Is the sequence 7, 14, 28, 56, ... arithmetic?

Is the sum of an infinite geometric series with |r| < 1 finite?

True or False: In an arithmetic sequence, the difference between any two consecutive terms is always constant.

True or False: The sequence 1, 2, 4, 8, 16, ... is a geometric sequence with common ratio 2.