Arithmetic Mean : Inclusive of NCERT examples Video Lecture | Mathematics for GRE Paper II

hello friends this video sequence and
series part 9 is brought to you by exam
calm before watching this video please
make sure that you have watched videos
part 1 to part 8 I will understand our
thematic - new concept so please be
teaching so we have been given two
numbers a and V that means in that is we
can insert a number E between them so
that a small a capital A and we are also
in a T so such number is called
arithmetic mean so we had told that we
have to number a and this is that
suppose a plus D so both are in a B now
we can insert a number X such that all
these number I a B so this will be
something a plus D by D so you insert a
Plus D by 2 what you get is a plus D by
2 and investing all this number a be
within now the D you change these become
divided and to get this number you
nothing but example you have a and B and
you are supposed to find X in a and B
are nay P and you want to find the X the
whole thing is an AP then X is nothing
less a plus B by from our last example
so we can see that X is going to do a
plus a plus D first and last term by 2
that is a plus D by so and this is
called mathematically or thematic mean
also means the mean of two numbers and
if you assume that both are in AP then
this is called a automatically so if
madam is adequate if you are given two
numbers we take the mean on the number
that becomes arithmetic mean
also it also means that if a and B are
in AP and or thematic mean whatever you
get for example a and B rdap
and the automatic mean of a B is KVM in
suppose so whatever you get take these
three numbers these humors are also very
easy as you also or thematic between the
automatic mean between two numbers a and
B is nothing but we'll take some
examples of Gotham adding me so here we
are told that we have to insert six
numbers between 3 and 24
or such that the resulting sequences
automatic rotation example the first
number is three sorry the first number
is three and second is nozzles 24 we are
supposed to insert six numbers
so it's insert a 1 e 2 e 1 e 2 e 3 E 4 E
5 a 6
let's assume that we are inserting these
six numbers between a and E such that or
thematic the whole thing is a B now this
thing if this whole sequence is a P you
observe that is equal to 2/3 that is
clear what is the value of n n is
nothing but 1 2 3 4 5 6 7 8 n is going
to eat correct this is what this is t8
so we know that T of 8 is going to a
plus n minus 1 D correct or T of 8 is 24
this has nothing but a is equal to 3 we
have proof plus n is equal to 8 minus 1
into D and this is nothing but 3 plus 7
D this is D so we have 7 D is nothing
but 24 minus 3 and this is nothing but
21 or D is 21 by 7 is equal to 3 so now
we have Big D's well two things will put
these vertically here so we have a + n D
so we can find all the terms example a 1
is nothing but t do this is t1 this is
t2 t2 a 1 is nothing but second term and
this is a + u minus 1 D that is a plus D
and that is 3 plus 3 that is 6 similarly
a 2 there is nothing but t3 is t3 t3 is
nothing but
a blurs 3-1 day and that is nothing but
a plus 2 D and that is 3 plus u into 3
that is 9
similarly a 4 a 3 a 3 is nothing but
full term fourth term is T 4 and this is
a plus 4 minus 1 D and this is e plus 3
D and this is 3 plus 3 into B is 3 that
is 12
similarly you will find a for if R is
nothing but v um t v and v of a 0 by a
plus 5 minus 1 D that is e plus 4 T and
if you put the value of a and D this
becomes e plus 4 into 3 and that comes
out to be 15 similarly a 5 is nothing
but 6 term and that is a plus 6 minus 1
D that is a plus 5 D and this is 3 plus
5 into 3 that is 80 similarly a 6 has
nothing but seventh term and this is a
plus 7 minus money group D that is a
plus 16 and that is 3 plus 6
so this becomes 3 plus 6 8 to 3 that is
18 plus 3 that is 21 so we have got all
this terms a 1 is equal to 6 9 12 15 18
21 we have all this term even a 2 a 3 a
4 a 5 a 6 right thank you
visit exam viacom to watch free
educational videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and much more thanks and sorry