Series

Q. find wrong number in series 4, 3, 6, 7, 8, 11, 10, 17, 13, 19

Q. How many terms of a GP $\frac{2}{3},\frac{-1}{3},\frac{1}{2}$..... should be added to get the sum equal to $\frac{55}{72}$?

1. 4
2. 5
3. 3
4. 6

Q. The sum of n terms of an arithmetic progression (AP) is $3n^2-n$.

(iv) If the sum of first n terms of this AP is 290, then the value of n is equal to:

[1 mark]

1. 7
2. 8
3. 9
4. 10

Q. If the roots of the equation $\left(a^2+b^2\right)x^2-2\left(ac+bd\right)x+c^2+d^2=0$ are real, then prove that
$ad=bc$

Q. Ramkali saved Rs. 5 in the first week of a year and then increased her weekly saving by Rs. 1.75. If in the $n^{th}$ week, her weekly savings become Rs 20.75, find n.

Q. There are four numbers such that first three of them from an A.P. and the last three form a G.P. The sum of the first and third number is 2 and that of second and fourth is 26. What are these numbers ?

Q. Find two consecutive whole numbers, such that $3$ times the first number plus $7$ times the second is $217$.

1. $19$ and $32$
2. $26$ and $40$
3. $17$ and $33$
4. $21$ and $22$

Q. Find the $n^{th}$ term of an A.P., sum of whose terms is $2n+3n^2$.

Q. Find the 9th term of the sequence 3, 11, 19, 27, .......

1. 64
2. 67
3. 72
4. 75

Q. In an $A.P.$ the 6th term is half the $4^{th}$ term and $3^{rd}$ term is $15$. How many terms are needed to give a sum that is equal to $66$?

Q. Next term of the series 2, -6, 18, -54 is ______

1. 162
2. -162
3. 486
4. -486

Q. Find the tenth term of the sequence specified by the recursion formula
$a_{k+1}=a_k+3$, if $a_1=7$.

Q. Find the nth term and the sum to n terms of the series for $1+5+13+29+61+....$

1. $T_n=2^{n+1}-3$
   $S_n=(2^2+2^3+2^{n+1})-3n$
2. $T_n=2^{n+1}+3$
   $S_n=(2^2+2^3+2^{n+1})+3n$
3. $T_n=2^{n+1}-3$
   $S_n=(2^2+2^3-2^{n+1})-3n$
4. $T_n=2^{n-1}+3$
   $S_n=(2^2+2^3+2^{n-1})+3n$

Q. In the sequence 1, 5, 9, 13, ... , the next term is ___

Q. Find the sum of all even natural numbers from $2$ to $40$.

Q. The shaded portion on a 24 hour clock given below tells the sleeping time of a sloth' (a bear). Find the time for which the sloth is asleep. Find the time for which the sloth is awake. If it sleep at 6 h 15 min then when does the sloth awake.

Q. Select which category the following sentence belongs to:
If we had gone to a better school, we would be able to enter a better university.

1. First Conditional
2. Zero Conditional
3. Second Conditional
4. Third Conditional

Q. Which number would replace the question mark in series
7, 12, 19, ?, 39

1. 24
2. 31
3. 26
4. 28

Q. The value of a if $4,a,25$ are in GP

1. $10$
2. $8$
3. $11$
4. $9$

Q. Which number would replace the question mark in series
7, 12, 19, ?, 39

1. 24
2. 31
3. 28
4. 26

Q. The arithmetic mean of first five natural number is

1. $3$
2. $4$
3. $5$
4. $6$

Q. Find a number which when divided by $39$ gives a remainder $16$ and when divided by $56$ gives a remainder $27$. How many such numbers are there?

Q. If $\frac{-2}{7},x,\frac{-7}{2}$ are in $G.P$, find $x$?

Q. Prove that the sum of n terms of series $\mathrm{1.3.5}+\mathrm{3.5.7}+\mathrm{5.7.9}+....$ is equal to
$n(2n^3+8n^2+7n-2).$

Q. Find the sum of $n$ terms of the series whose $n^{th}$ term is
$3^n-2^n$.

Q. The sum of the series $\frac{1}{{\log }_{2}4}+\frac{1}{{\log }_{4}4}+\frac{1}{{\log }_{8}4}+...+\frac{1}{{\log }_{2^n}4}$ is equal to

1. $\frac{n(n+1)}{4}$
2. $\frac{n(n+1)(2n+1)}{12}$
3. $\frac{1}{n(n+1)}$
4. $\frac{n(n+1)}{2}$

Q. The sum of 3 positive numbers in AP is 189. The sum of their squares is 11915. Find their product.

1. 7930
2. 9703
3. 7960
4. 8970
5. None of these

Q. If A be the A.M. and G be the G.M. between two numbers . Show that the numbers are given by $A\pm \sqrt{A^2-G^2}$

Q. The square of 35 is

Q. Sum of the series $\sum _{r=1}^n(r^2+1)r!$ is

1. $(n+1)!$
2. $(n+2)!-1$
3. $n\cdot (n+1)!$
4. $n\cdot (n+2)!$