Sequences and Series
What is the 10th term of the arithmetic progression (A.P.) 2, 7, 12, ...?
If the sum of $n$ terms of an A.P. is given by $S_n = 3n^2 + 5n$, then find its 2nd term.
What is the 5th term of the geometric progression (G.P.) 3, 6, 12, ...?
Which term of the G.P. 2, 4, 8, 16, ... is 512?
What is the arithmetic mean (A.M.) between 4 and 20?
What is the geometric mean (G.M.) between 2 and 8?
If the sum of $n$ terms of a series is $S_n = 2^n - 1$, what type of sequence does it represent?
Find the sum of the first 20 terms of the arithmetic progression 1, 3, 5, 7, ...
What is the sum of an infinite geometric series with first term $a = 1$ and common ratio $r = \frac{1}{2}$?
If $a, b, c$ are in A.P., then which of the following relations is always true?
If $a, b, c$ are in G.P., which of the following is true?
What is the 7th term of the sequence defined by $a_n = (-1)^{n-1} n^3$?
If the sum of $n$ terms of a G.P. is given by $S_n = a\frac{r^n - 1}{r - 1}$, then this formula is valid when:
What is the sum of the first $n$ natural numbers?
If the 4th term of a G.P. is 8 and the 7th term is 64, what is the first term $a$?
What is the common ratio of the G.P. $\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, ...$?
If $1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, ...$ is a sequence, what type of sequence is it?
What is the 20th term of the A.P. whose first term is 5 and common difference is 3?
If the sum of three numbers in G.P. is 38 and their product is 1728, what are the numbers?
Which of the following is a sequence whose terms are formed by the rule $a_n = 2n + 1$?