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 10

Find the 6th term of the sequence defined by aₙ = 2n + 1.

Find the 7th term of the geometric sequence: 3, 6, 12, ...

Find the 8th term of the arithmetic sequence: 10, 7, 4, ...

Find the common ratio of the geometric sequence: 81, 27, 9, 3, ...

Find the sum of the first 10 terms of the arithmetic sequence: 1, 4, 7, ...

Find the sum of the first 6 terms of the geometric sequence: 2, 4, 8, ...

Find the sum to infinity of the geometric series: 4, 2, 1, ...

Consider the sequence: 5, 8, 13, 20, 29, ... What is the next term in the sequence?

If a sequence has a constant second difference, what type of sequence is it most likely to be? (1) Arithmetic (2) Geometric (3) Quadratic (4) Harmonic

Which formula is used to find the nth term of a geometric sequence? (1) aₙ = a₁ + (n-1)d (2) aₙ = a₁ × r^(n-1) (3) aₙ = a₁ / n (4) aₙ = n × a₁

Which of the following is a property of a geometric sequence? (1) Each term is the sum of the previous term and a constant. (2) Each term is the product of the previous term and a constant. (3) Each term is the square of the previous term. (4) Each term is the difference of the previous term and a constant.

Which of the following is an arithmetic sequence? (1) 2, 4, 6, 8 (2) 3, 6, 12, 24 (3) 5, 10, 20, 40 (4) 7, 14, 21, 28

Fill in the blank: In a geometric sequence, the nth term is given by aₙ = a₁ × _________.

Fill in the blank: In a sequence, each number is called a _________.

Fill in the blank: The difference between consecutive terms in an arithmetic sequence is called the _________.

Fill in the blank: The first term of a sequence is called the ________ term.

True or False: In a geometric sequence, the ratio between consecutive terms is always constant.

True or False: The sequence 1, 1/2, 1/4, 1/8, ... is a geometric sequence.

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

True or False: The sequence 1, 3, 6, 10, 15, ... is an arithmetic sequence.