subject

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 a_1 = 1. Find a_4.
A sequence is defined by a_n = n^2 + 1. What is the 6th term?
A sequence is defined recursively by a_1 = 2, a_{n+1} = 3a_n + 1. Find a_3.
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?
If the sum of the first 5 terms of a geometric sequence is 62 and the first term is 2, what is the common ratio?
If the sum of the first n terms of a sequence is S_n = 3n^2 + 2n, what is the 4th term?
If the sum of the first n terms of a sequence is S_n = n(n+1), what is the nth term?
The sum of the first 10 terms of an arithmetic sequence is 145. If the first term is 5, what is the common difference?
A geometric sequence has positive terms. If the 2nd term is 12 and the 5th term is 96, what is the common ratio?
Consider the sequence defined by a_1 = 2, a_{n+1} = a_n + 3n for n \geq 1. Find a formula for a_n in terms of n.
Given the sequence defined by a_1 = 5, a_2 = 11, and a_n = 4a_{n-1} - 4a_{n-2} for n \geq 3, find a general formula for a_n.
If the sum of the first n terms of a geometric sequence is S_n = 81(1 - (1/3)^n)/ (1 - 1/3), what is the first term of the sequence?
If the sum of the first n terms of a sequence is S_n = 2n^3 + 3n^2 + n, find the 5th term of the sequence.
The sum of the first n terms of an arithmetic sequence is given by S_n = 7n^2 + 2n. Find the common difference of the sequence.