1. Sum of the series $\frac{5}{(13)^{1}}+\frac{55}{(13)^{2}}+\frac{555}{(13)^{3}}+\frac{5555}{(13)^{4}}+...$ up to $\infty$ is:
2. Arithmetic mean between $2+\sqrt{2}$ and $2-\sqrt{2}$ is:
3. If $\frac{1}{a},\frac{1}{b}$ and $\frac{1}{c}$ are in G.P then common ratio is equal to_________
4. A.M between $\frac{a}{2}$ and $\frac{2}{a}$ is
5. If the nth term of an A.P is $\frac{1}{2}(3-n)$ then first three terms are _________
6. Sum of $n$ terms of an A.P is ____
7. If $\frac{1}{5}, \frac{1}{8}$ are two H.M between $\frac{1}{2}$ and $b$ then be equals to
8. If $a_{1}$ and $r$ are the first term and common ratio respectively then the $(n+1)^{th}$ term of G.P is________
9. If $a,b,c$ are in A.P, then $3^{a},3^{b},3^{c}$ are in:
10. $\sum_{k=1}^{n} 5$ is equal to:
11. An arithmetic progression has a first term 12 and a fifth term 18, then the sum of first 25 term is.
12. The arithmetic mean in the sequence $-7$,_,_,$5$ are
13. The series $1+\frac{x}{2}+\frac{x^2}{4}+...$ is convergent if________
14. The $10^{th}$ term of $\frac{1}{2},\frac{1}{5},\frac{1}{8},...,$ is:
15. If $a_{n-2}=3n-11$ then nth term is
16. In geometric sequence nth term equal to
17. $\sum_{k=1}^{n} k^{2}=?$ or $(1^2+2^2+3^2+...+n^2)=?$
18. For an infinite geometric series for which $|r|
19. If $a,b$ are negative then $G.M$ is:
20. In the sequence $1,2,2,3,3,3,4,4,4,4,...$ where n-consecutive terms have the value n, the $22^{nd}$ term is:
21. The sum $\sum_{r=2}^{\infty} \frac{1}{r^2-1}$ represents:
22. Sequence is denoted by______
23. The $(n+1)th$ term of an A.P is _______
24. Geometric mean of Two positive numbers a and b
25. $a_{n}=\frac{(-1)^{n+1}}{2^{n}}$, then $a_{6}=?$
26. The reciprocal of the term of H.P is.....
28. An arithmetic series $S_{n}$ equals to ____
29. For what value of $n$, $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$ is the A.M between a and b?
30. If $\frac{1}{a},\frac{1}{b}$ and $\frac{1}{c}$ are in A.P then b is equal to_________.
31. $0.1+0.01+0.001+0.0001+....$ the sum is:
32. Find first term of the geometric series, when $S_{n}=30,n=4,r=-2$
33. If A,G,H have their usual meanings and 'a' and 'b' are positive distinct real numbers and $G>0$, then:
34. The general term of the given series $\frac{1}{1.3}+\frac{1}{2.5}+\frac{1}{3.7}+...$ is
35. $\sum_{j=1}^{10} \sum_{i=1}^{15} k =?$
36. What is sum of n term with nth term $a_{n} = 4n+1$
37. In $\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+$...., then $n^{th}$ term is:
38. A sequence $a_{n}$ is an arithmetic sequence if $\forall \, n\in\,\mathbb{N}$ and $n>1$:
39. Let $a,b$ be two positive numbers, where $a>b$ and $4\times\,G.M=5\times\,H.M$ for the numbers, the a is:
40. The sigma notation for the sum $-2+4-6+8$ is:
41. If $\frac{4}{7}$ be the third term of H.P, then third term of A.P is:
42. $\sum_{k=1}^{n} k=?$ or (sum of first n terms)
43. An infinite sequence has no __________
44. $S_{n}=1+2+3+...+n$ can also be shown as_______
45. If $\frac{1}{a},\frac{1}{b}$ and $\frac{1}{c}$ are in A.P then common difference is equal to_________.
47. Sum of the series $1+3+5+7+9+11+...+n$ terms is:
48. The formula $S_{n}=\frac{a(r^{n}-1)}{r-1}$ is used for sum of a terms of G.P. if ____
49. If $a,A,b$ are in A.P then $2A=?$
50. $\sum_{k=1}^{n} k^{3}=?$ or $(1^3+2^3+3^3+...+n^3)=?$
51. The nth term of an A.P with usual notions is ______
52. Predict the general term for the sequence $\frac{4}{3},\frac{4}{9},\frac{4}{27},\frac{4}{81},...$
53. Arithmetic Mean between two numbers $\frac{1}{a}$ and $\frac{1}{b}$ is:
54. Sum of $n$ arithmetic means between a and b is ________
55. Find the $26^{th}$ terms from the end of A.P : $2,7,12,17,...,222.$
56. If $a,b,c$ are in G.P and $a>0,b>0,c>0,$ then the reciprocals of $a,b,c$ form ______
57. $\frac{1}{k}, \frac{1}{2k+1}, \frac{1}{4k-1}$ are in H.P then $k=?$
58. An infinite geometric series is convergent if _____
59. The next term of G.P. $1,2,4,8,16,...$ is:
60. G.Ms between $1$ and $\frac{1}{3}$ is:
61. If $x,y,z$ are in H.P. Sequence then value of z is ______
62. The nth term of sequence $\frac{1}{3},\frac{2}{5},\frac{3}{7},....$ is:
63. If $y=\frac{2}{3}x+\frac{4}{9}x^2+\frac{8}{27}x^3+....$ then interval of convergence is____
64. What is the sum of infinite G.P; $2,\sqrt{2},1,...?$
65. The A.M between two numbers a and b is ________
66. $\sum_{k=1}^{3} k^2$ is equal to:
67. Which term of $64,60,56,52,...$ is zero?
68. If $a_{n}-a_{n-1}=n+2$, $a_{1}=2$ then $a_{3}=?$
69. How many terms of sequence $18,15,12,....$ are needed to give a sum of 63?
70. $a_{5}$ in G.P $3,6,12,...$ will be _____
