Sequences and Series in Calculus

Math ⇒ Calculus

Sequences and Series in Calculus starts at 11 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 in Calculus. 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 geometric sequence has a first term of 6 and a common ratio of 0.5. What is the 4th term?

Find the 10th term of the sequence 3, 7, 11, 15, ...

Find the 12th term of the arithmetic sequence 4, 9, 14, ...

Find the 7th term of the geometric sequence 1, 3, 9, 27, ...

Find the sum of the first 5 terms of the sequence defined by a_n = 2n - 1.

Find the sum of the first 6 terms of the arithmetic sequence 2, 5, 8, ...

Find the sum of the infinite geometric series 10 + 5 + 2.5 + ...

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

The sequence defined by a_n = 2n + 3 is: (1) Arithmetic (2) Geometric (3) Neither (4) Both

Which of the following is a necessary condition for the convergence of an infinite geometric series? (1) |r| > 1 (2) |r| = 1 (3) |r| < 1 (4) r = 0

Which of the following is NOT a property of arithmetic sequences? (1) The difference between consecutive terms is constant. (2) The ratio between consecutive terms is constant. (3) The sequence can be increasing or decreasing. (4) The nth term can be found using a linear formula.

Which of the following is the general term of the geometric sequence 3, 6, 12, 24, ...? (1) a_n = 3n (2) a_n = 3 × 2^n-1 (3) a_n = 2 × 3^n-1 (4) a_n = 6n

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

Fill in the blank: The infinite geometric series a + ar + ar² + ... converges if |r| < ____.

Fill in the blank: The sequence a_n = 1, 1/2, 1/3, 1/4, ... is called the _______ sequence.

Fill in the blank: The sequence a_n = 2ⁿ is a _______ sequence.

True or False: Every bounded sequence is convergent.

True or False: Every convergent sequence is bounded.

True or False: The harmonic series 1 + 1/2 + 1/3 + 1/4 + ... converges.

True or False: The sequence a_n = (-1)ⁿ/n converges.