Sequences and Series in Calculus
Math ⇒ Calculus
Sequences and Series in Calculus starts at 11 and continues till grade 12.
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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 + \ldots
Find the sum of the infinite geometric series 4 + 2 + 1 + \ldots
If a sequence is defined by a_n = 5 - 2n , what is the 8th term?
If a sequence is defined recursively by a_1 = 1,\, a_{n+1} = a_n + 3 , what is a_6 ?
If a sequence is defined recursively by a_1 = 2,\, a_{n+1} = 3a_n , what is a_4 ?
If the first term of an arithmetic sequence is 7 and the 5th term is 23, what is the common difference?
If the sum of an infinite geometric series is 8 and the first term is 2, what is the common ratio?
If the sum of the first 5 terms of an arithmetic sequence is 40 and the first term is 4, what is the common difference?
If the sum of the first n terms of a sequence is S_n = 3n^2 , what is the 5th term?
If the sum of the first n terms of a sequence is S_n = n(n+1) , what is the nth term?
What is the general term (n-th term) of the arithmetic sequence with first term a and common difference d ?
What is the sum to infinity of the geometric series 5 + 2.5 + 1.25 + \ldots ?
Determine whether the series \sum_{n=1}^{\infty} \frac{2^n}{3^n} converges or diverges. Justify your answer.
Given the infinite geometric series 7 + 2.1 + 0.63 + \ldots , find its sum.
