IMG_20180830_131233_931.JPG sir question 3and 5 If an=sin(n pi)/6 then the value of sigma from n=1 to 6 a^2n
If a1 =2, a2 =3+ al and an = 2 an _ 1 + 5 for n > 1, then t
value of a20 is
(a) 65
(c) 87
(a) 130
(b) 75
(d) 97
(b) 160

@ Roshni Afrin

IMG_20190124_233406.jpg EXANII'LE 21 The
Of
deviation
a, a + d, a + 21,
a + (2n 1) d, a + 2nd about the tncan is
(a)
Ans. (b)
(b)
(c)
SOLUTION The mean of the given series is a + nd. (See
chapter 52).
Mean deviation about mean
1
I (a + rd) (a + nd) I
(211 + 1)
2n
d
n
11 (11 + 1)
x
2
211 + 1

@Shyam Both of the summation terms will be equal as | r - n | gives same values in interval [1,n] & [n,2n] so you can write the summation as double of summation from 1 to n.

Let be a G.P. If then equals :

- Option 1)
- Option 2)
- Option 3)
- Option 4)

Geometric Progession (GP) -
A progression of non - zero terms, in which every term bears to the preceding term a constant ratio.
- wherein
eg 2, 4, 8, 16,- - - - - -
and
100, 10, 1, 1/10,- - - - - - -
General term of a GP -
- wherein
first term
common ratio
Let first term of G.D be a and common ratio = r
Now, Option 1)
Option 2)
Option 3)
Option 4)

If 19th term of a non-zero A.P. is zero, then its ( 49th term ) : ( 29th term ) is :

- Option 1)
2:1

- Option 2)
4:1

- Option 3)
3:1

- Option 4)
1:3

General term of an A.P. -
- wherein
First term
number of term
common difference
Option 1)2:1Option 2)4:1Option 3)3:1Option 4)1:3

Let x,y be positive real numbers and m,n positive integers. The maximum value of the expression is :

- Option 1)
1

- Option 2)
- Option 3)
- Option 4)

Relation between AM, GM and HM of two positive numbers -
- wherein
Inequality of the three given means.
1
Option 1)
1Option 2)Option 3)
Option 4)

The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is

Then the common ratio of this series is :

- Option 1)
- Option 2)
- Option 3)
- Option 4)

Sum of infinite terms of a GP -
- wherein
first term
common ratio
Lrt first term of G.P is a and the common ratio is r (r<1)
Given, 2)
Given, 2)
From (1) and (2)
since r<1
Option 1)
Option 2)
Option 3)
Option 4)

If the sum of the first 15 terms of the series

is equal to 225 k, then k is equal to :

- Option 1)
- Option 2)
- Option 3)
- Option 4)

Summation of series of natural numbers -
- wherein
Sum of first n natural numbers
Summation of series of natural numbers -
- wherein
Option 1)
Option 2)
Option 3)
Option 4)

If , , and are in A.P., then n can be :

- Option 1)
- Option 2)
- Option 3)
- Option 4)

Arithmetic mean of two numbers (AM) -
- wherein
It is to be noted that the sequence a, A, b, is in AP where, a and b are the two numbers.
Option 1)Option 2)Option 3)Option 4)

Let be in GP with for and S be the set of pairs (r, k), r, k( the set of natural numbers) for which

Then the number of elements in S, is:

- Option 1)
4

- Option 2)
Infinitely many

- Option 3)
10

- Option 4)
2

Geometric Progession (GP) -
A progression of non - zero terms, in which every term bears to the preceding term a constant ratio.
- wherein
eg 2, 4, 8, 16,- - - - - -
and
100, 10, 1, 1/10,- - - - - - -
General term of a GP -
- wherein
first term
common ratio
Apply coloumn operation
we get D = 0
OR
are in G.P.
assume
Since are in G.P. with common ratio 1
So,
Value of D become...

The sum of all two digit positive numbers which when divided by 7 yeild 2 or5 as remainder is :

- Option 1)
1256

- Option 2)
1465

- Option 3)
1365

- Option 4)
1356

Summation of series of natural numbers -
- wherein
Sum of first n natural numbers
From the concept ,
General term will be
total = 1356Option 1)1256Option 2)1465Option 3)1365Option 4)1356

Let If then A is equal to :

- Option 1)
- Option 2)
- Option 3)
- Option 4)

Summation of series of natural numbers -
- wherein
Sum of first n natural numbers
Since
Option 1)Option 2)Option 3)Option 4)

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :

- Option 1)
- Option 2)
- Option 3)
- Option 4)

Selection of terms in G.P. -
If we have to take three terms in GP, we take them as
- wherein
Extension : If we have to take (2K+1) term in GP, we take them as
General term of an A.P. -
- wherein
First term
number of term
common difference
be three terms.
Putting
Numbers are 4,8,16 or 16, 8,4
Sum of numbers = 4+ 8 + 16 = 28Option 1)Option 2)Option 3)Option 4)

Let a,b and c be the 7th,11th and 13th terms respectively of a non-constant A.P.If these are also the three consecutive terms of a G.P., then a/c is equal to :

- Option 1)
2

- Option 2)
7/13

- Option 3)
1/2

- Option 4)
4

General term of an A.P. -
- wherein
First term
number of term
common difference
Selection of terms in G.P. -
If we have to take three terms in GP, we take them as
- wherein
Extension : If we have to take (2K+1) term in GP, we take them as
From the concept
and and are in G.P
Option 1)
2Option 2)
7/13Option 3)
1/2Option 4)
4

Let S be the set of all triangles in the xy-plane,each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangles is S has area 50 sq. units, then the number of the elements in the set S is:

- Option 1)
9

- Option 2)
32

- Option 3)
18

- Option 4)
36

Number of Divisions -
The number of divisors of a natural number
is
- wherein
Where a1, a2 ....... are distinct prime and non negative integers.
Let
and be vectors of
Area of le is
Number of triangles
Option 1)
9Option 2)
32Option 3)
18Option 4)
36

The sum of the following series

up to 15 terms, is:

- Option 1)
7830

- Option 2)
7820

- Option 3)
7510

- Option 4)
7520

Summation of series of natural numbers -
- wherein
Sum of first n natural numbers
Summation of series of natural numbers -
- wherein
Sum of squares of first n natural numbers
Summation of series of natural numbers -
- wherein
The general term of the sequence will be
Option 1)
7830Option 2)
7820Option 3)
7510Option 4)
7520

Let be an AP, and .

If and

then is equal to:

- Option 1)
52

- Option 2)
57

- Option 3)
47

- Option 4)
42

Sum of n terms of an AP -
and
Sum of n terms of an AP
- wherein
first term
common difference
number of terms
Last term of an A.P.(l) -
- wherein
If a series has n terms last term is
Summation of terms of an AP
or,
Now,
Now use,
Give
Now,
Option 1) 52Option 2)57Option 3)47Option 4)42

If a, b and c be three distinct real numbers in G.P and then cannot be:

- Option 1)
-2

- Option 2)
-3

- Option 3)
4

- Option 4)
2

General term of a GP -
- wherein
first term
common ratio
from the concept we have learnt
Let the three terms be
given
from the AM-GM
So,
So, Option 1)-2Option 2)-3Option 3)4Option 4)2

As we can see, the general term of the sequence is
Hence The sum :
Now, putting n = 15, we get

Please, help me to get out of this problematic question... If a/b=2/3 and b/c=4/5, then find the value of (a+b)/(b+c)

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