Sum of n Terms

Q. Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, .

Q.

If $f\left(x\right)=\log \left[\frac{(1+x)}{1-x}\right]$, where $-1<x<1$, then $f\left[\frac{(3x+x^3)}{(1+3x^2)}\right]-f\left[\frac{\left(2x\right)}{(1+x^2)}\right]$ is equal to

1. ${\left[f\right(x\left)\right]}^3$

2. $\left[f\right(x){]}^2$

3. $-f\left(x\right)$

4. $f\left(x\right)$

5. $3f\left(x\right)$

Q.

Find a formula for $S_n$, the sum of the first $n$ terms of the geometric sequence.

Q.

The first term of an AP is a and the sum of the first p terms is zero, show that the sum of its next q terms is $\frac{-a(p+q)q}{p-1}$

Q.

A farmer buys a used tractor for Rs. 12000. He pays Rs. 6000 cash and agrees to pay the balance in annual instalments of Rs. 500 plus $12\%$ interest on the unpaid amount. How much will the tractor cost him ?

Q. In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20 th term is –112.

Q.

The n^th term (general term) of an arithmetic progression, a₁, a₂, a₃, …, a_n, … where a₂ –a₁ = a₃ – a₂ = …. = d is:

1. a_n = a₁ – (n – 1)d

2. a_n = a_n-1 – (n – 1)d

3. a_n = a₁ + (n – 1)d

4. a_n = a_n-1 + (n-1)d

Q. mod of x minus 3 plus mod of 4 minus x is equal to 1 . find the value of x

Q. 21. rth term of a series is the sum of rth terms of an A.P. and rth term of a G.P.; whose first terms are equal to one each and the common difference of the A.P. and common ratio of the G.P. are equal to n each, n N. Number of such terms in this series which are perfect squares of a natural number for all n, is

Q. The sum of 4 consecutive numbers in an AP is 32 and the ratio of the product to the first and the last term to the product of the two middle terms is 7:15.Find the numbers?

Q. The sum of all natural number between 100 and 300 which when divided by 4 leaves remainder 3 is .

1. 5025
2. 5050
3. 10050
4. 10100

Q.

The sum of the series a-(a+d)+(a+2d)-(a-3d)+....upto (2n+1) terms is

1. -nd

2. a+2nd

3. a+nd

4. 2nd

Q.

If A₁, A₂, A₃, ...., A_n are n numbers between a and b, such that a, A₁, A₂, A₃, ..., A_n, b are in A.P., then the common difference of this A.P. is:

1. 

2. 

3. 

4. 

Q.

In the chess championship, $153$ games have been played. If a player with every other player plays only once, then the no. of players are?

1. $17$

2. $51$

3. $18$

4. $35$

Q. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

Q. 46. The sum of infinite number of term of a decreasing G.P is 4 and the sum of the square of its term to infinity is 16/3 , find the G.P

Q.

If the bisector of angles represented by $a{x}^2+2hxy+b{y}^2=0$ and $a^{{}^{\prime }}{x}^2+2h^{{}^{\prime }}xy+b^{{}^{\prime }}{y}^2=0$ are same, then

1. 

2. 

3. 

4. 

Q.

Find the sum to 20 terms in the geometric progression
0.15, 0.015, 0.0015 ...

Q. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

Q. 34. A G. P. consists of 2n terms. If the sum of the terms occupying the odd places is S1 and that of the terms occupying the even places is S2, then find the common ratio of the progression.

Q. If the sum of n terms of an A.P. is ( pn + qn 2 ), where p and q are constants, find the common difference.

Q. Let, $S_n$ denote the sum of first $n$ terms of an arithmetic progression whose first term is $-4$ and common difference is $1$. If $V_n=2S_{n+2}-2S_{n+1}+S_n(n\in N)$, then the minimum value of $V_n$ is

1. $-1$
2. $9$
3. $-9$
4. $-\frac{73}{8}$

Q. If, in a $G.P.$ of $3n$ terms, $S_1$ denotes the sum of the first $n$ terms, $S_2$ the sum of the second block of $n$ terms and $S_3$ the sum of the last $n$ terms, then $S_1,S_2,S_3$ are in

1. $A.P.$
2. $G.P.$
3. $H.P.$
4. $A.G.P.$

Q.

Express the complex numbers in the form of a + ib:

$(\frac{1}{5}+\frac{2}{5}i)-(4+\frac{5}{2}i)$

Q. If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first ( p + q ) terms.

Q.

Find the value of ${}^{15}{C}_2$+ 2 ${}^{15}{C}_3$ + 3 ${}^{15}{C}_4$ . . . . . 14 ${}^{15}{C}_{15}$

__

Q.

What is the next term In the sequence $-8,-5,-2,$?

Q. let the function f be defined by f(x)=x/(e^{-x} -1)+x/2+5 then f(x) is (evrn function, odd function, periodic function

Q.

The ratio of the sum of n terms of two A.P's is (7n + 1) : (4n + 27). The ratio of their 12^thterms is:

1. 176 : 127

2. 162 : 119

3. 155 : 115

4. 169 : 123

Q.

If $-\frac{\pi }{2}<x<\frac{\pi }{2}$ and the sum to infinite number of terms of the series$cosx+\frac{2}{3}cosxsi{n}^{2}x+\frac{4}{9}cosxsi{n}^{4}x+.....$ is finite, then $x$ lies in the set

1. $-\frac{\pi }{2}<x<\frac{\pi }{2}$

2. $-\frac{\pi }{6}<x<\frac{\pi }{6}$

3. $\frac{\pi }{6}<x<\frac{\pi }{2}$

4. $0<x<\frac{\pi }{2}$