JEE-Main - Grade 11 - Mathematics - Sequences and Series - Importance and Snapshot of Sequences and Series - Study ref# 626

Introduction
In mathematics this words, “sequence” is used in much the
same way as it is in ordinary English. When we say that a collection of
objects is listed in a sequence, we usually mean that the collection is
ordered in such a way t... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Importance and Snapshot of Sequences and Series - Study ref# 627

Following sections must be covered to understand Sequences and Series:
1. Sequences
2. Series
3. Arithmetic Progression (A.P.)
4. Geometric Progression (G.P.)
5. Relation between A.P. and G.P.
6. Sum to n Terms of Special Series... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Target Setup for Sequences and Series - Study ref# 628

Student requires to achieve the following milestones to get better grip over Sequence and Series. The milestones / targets are as follows:-Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapter Test000%... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5265

Write the first five terms of the sequence Answer: We have,
Substituting n= 1, 2, 3,4,5, we get
∴
The first five terms are ... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5266

Write the first five terms of the sequence Answer: We have,
Substituting we
get
.
∴
The first five terms are 2,4,8,16,32.... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5267

Write the first five terms of the sequence Answer: We have,
Substituting we
get
∴
The first five terms are .... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5268

Find the indicated terms in the sequence Answer: We have,
Put
Put .... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5269

Write the first five terms of the provided sequence and obtain the corresponding series for all
n >1 Answer: We have given ,
Hence the first five terms of the sequence are
3,11,35,107,323.
The co... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5270

The Fibonacci sequence is defined by and . Find , for Answer: We have,
Now, substitute in
,
we obtain
... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5271

Find the sum of odd integers from 1 to 2001. Answer: We have to find 1 + 3 + 5 + ……..+ 2001.
This is an A.P. with first term common difference and last term
... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5272

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. Answer: Let be
the first term and d be the common difference.
∴
Sum of first five terms
... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5273

In an A.P., if term
is and term is , prove that the
sum of first pq terms is where
. Answer: Let a be the first term & d be the common difference
of the A.P., then
………(i)
………(ii)
From (i) ... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5274

If the sum of n terms of an A.P. is , where p and q
are constants, find the common difference. Answer: We have where
be the sum of n
terms.
(sum of
1 term i.e., first term)
(sum of
2 terms i.e., sum of first term & seco... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5275

If the sum of first p terms of an A.P. is equal to the sum
of first q terms, then find the sum of the first (p + q) terms. Answer: Let the first term be a and common difference be d.
According to question
... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5276

Insert five numbers between 8 and 26 such that the
resulting sequence is an A.P. Answer: Let be
numbers between 8 and 26 such that 8, 26 are in A.P.,
Here
Thus
He... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5277

If is
the A.M. between a and b, then find the value of n. Answer: We have =
.... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5278

A man starts repaying a loan as first instalment of Rs.
100. If he increases the instalment by Rs.5 every month, what amount he will
pay in the 30th instalment ? Answer: Here, we have an A.P. with a = 100 and d = 5
Hence he will pay Rs ... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5279

The difference between any two consecutive interior angles
of a polygon is 5°. If
the smallest angle is 120°, find
the number of the side of polygon. Answer: Let there are n sides of a polygon.
Then sum of all interior angles = read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5280

Find the 12th term of a G.P. whose 8th
term is 192 and the common ratio is 2. Answer: We have
Now, ... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5281

The 5th, 8th and 11th
terms of a G.P. are p, q and s, respectively. Show that . Answer: We are given
……..(i)
……..(ii)
…….(iii)
Now multiplying (i) and (iii), we get
[using
(ii)]
... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5282

Which term of the following sequences:
(a) is
128?
(b) is
729 ?
(c) is
? Answer: (a) Let 128 be the term of the given
G.P. Here and
Therefore,
... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5283

Find the sum to indicated number of terms in the provided geometric progression terms. Answer: In the given G.P.
, if
=
.... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5284

Find the sum to indicated number of terms in the provided geometric progression terms
(if ). Answer: In the given G.P. ,
and if
... read more

JEE-Main - Grade 11 - Mathematics - Sequences and Series - Study ref# 5285