Quiz on Sequence & Series

GOUTHAM SANKEERTHMaths

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AKSHAY ARORA

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Maths

“Your best teacher is your last mistake.”

– Dr APJ Abdul Kalam

Quote

Homework

Find the sum to 𝑛 terms of the series :

12 + 12 + 22 + 12 + 22 + 32 +⋯

Homework

Find 1

1∙2+

1

2∙3+

1

3∙4+⋯ upto n terms.

Scope

S. No Name Of Concept Number Of Questions

1 Problems on AP 8

2 Problems on GP 4

3 Problems on AP GP 4

4 Problem on Infinite GP 3

5 Problem on AM GM 5

6 Special Series 10

7 Miscellaneous Problems 4

Analysis of the Number of Questions asked in JEE

Mains from 2013-20

Solve

Let a1, a2, a3, ….. be a sequence of positive integers in arithmetic

progression with common difference 2. Also, let b1, b2, b3, ….. be

a sequence of positive integers in geometric progression with

common ratio 2. If a1 = b1 = c, then the number of all possible

values of c, for which the equality 2(a1 + a2 + ….+an ) = b1 + b2 +

….. + bn holds for some positive integer n, is ______ JEE

Advance 2020

Solve

If 100 times the 100th term of an AP with non-zero common

difference equal to the 50 times its 50th term, then the 150th term

of this AP is JEE M 2012

(a) -150 (b) 150 times its 50th term (c) 150 (d)

zero

Solve

Let the sum of the first three terms of an AP be 39 and the sum of

its last four terms be 178. If the first term of this AP is 10, then the

median of the AP is JEE M 2015

(A) 26.5 (B) 28 (C) 29.5 (D) 31

Solve

Let a1,a2,a3,....., an ...... be in A.P. If a3+ a7+ a11 +a15 = 72, then the

sum of its first 17 terms is equal to : JEE M 2016

(a) 306

(b) 153

(c)612

(d) 204

Solve

Let a1, a2, .....,a30 be an A.P., S = Σai i ∈[i = 1, 30] and T = Σ a(2i-1) i ∈ [i

= 1, 15] If a5 = 27 and S – 2T = 75, then a10 is equal to JEE M 2019- Jan

(1) 47 (2) 52 (3) 57 (4) 42

Solve

Let f : R → R be such that for all x ∈ R (21 + x + 21 - x), f(x) and (3x +

3-x) are in A.P. then the minimum value of f(x) is JEE M 2020- Jan

(1) 0 (2) 3 (3) 2 (4) 4

Solve

The number of terms common to the two A.P. 's 3, 7, 11, ....., 407

and 2, 9, 16, ....., 709 is ______. JEE M 2020- Jan

Solve

The sum of the 3rd and the 4th terms of a G.P. is 60 and the

product of its first three terms is 1000. If the first term of this G.P.

is positive, then its 7th term is : JEE M 2015

(1) 7290 (2) 640 (3) 2430 (4) 320

Solve

If a, b and c be three distinct real numbers in G.P. and a + b + c =

xb, then x cannot be JEE M 2019- Jan

(1) –3 (2) –2 (3) 2 (4) 4

Solve

If three distinct numbers a, b, c are in G.P. and the equations

ax2 + 2bx + c = 0 and dx2 + 2ex + f = 0 have a common root, then

which one of the following statements is correct ? JEE M 2019-

Apr

(1) d, e, f are in A.P. (2) d/a, e/b, f/c are n A.P

(3) d, e, f are in G.P (4) d/a, e/b , f/c are n G.P

Solve

Let a1, a2, a3,… be a G.P. such that a1 < 0, a1 + a2 = 4 and a3 + a4

= 16. If ∑ai = 4λ, i ∈ [i = 1, 9], then λ is equal to : JEE M 2020- Jan

(1) –171 (2) 171 (3) 511/3 (4) -513

Solve

Three positive numbers form an increasing GP. If the middle term in

this GP is doubled, then new numbers are in AP. Then, the common

ratio of the GP is JEE M 2014

(a) √2 + √3 (b) 3 + √2 (c) 2 - √3 (d) 2 + √3

Solve

Let a, b and c be in G.P. with common ratio r, where a ≠ 0 < r ≤

1/2. If 3a, 7b and 15c are the first three terms of an A.P., then the

4th term of this A.P. is : JEE M 2019- Apr

(1) a (2) 7/3 a (3) 2/3 a (4) 5a

Solve

If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the following series (x+y) + (x2+xy+y2) + (x3+x2y + xy2+y3)+..... JEE M 2020- Sept(a) (x + y + xy)/ (1+x)(1+y)(b) (x + y –xy)/ (1-x) (1-y)(c) (x + y –xy)/ (1+x) (1+y)(d) (x + y +xy)/ (1-x) (1-y)

Solve

Let x, y, z be positive real numbers such that x + y + z = 12 and

x3y4z5 = (0.1)(600)3. Then, x3 + y3 + z3 is equal to JEE M 2017 ‘(A) 342 (B) 216 (C) 258 (D) 270

Problems On AM- GM

Solve

The minimum value of 2sin x + 2cos x is :- JEE M 2020- Sept

(1) 21 - (1/√2) (2) 2-1 + √2 (3) 21 - √2 (4) 2-1 + (1/√2)

Solve

The sum of first 9 terms of the series 13/1 + (13 + 23)/(1 + 3) + (13 + 23 +

33)/(1 + 3 + 5) + ... is JEE M 2015

(a) 71 (b) 96 (c) 142 (d) 192

Solve

The greatest positive integer k, for which 49k + 1 is a factor of the

sum 49125 + 49124 + ... 492 + 49 + 1, is : JEE M 2020- Jan

(1) 32 (2) 60 (3) 63 (4) 65

Solve

Let a,b,c,d and p be any non zero distinct real numbers such that (a2 + b2

+ c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then : JEE M 2020- Sept

(1) a,c,p are in G.P. (2) a,c,p are in A.P.

(3) a,b,c,d are in G.P. (4) a,b,c,d are in A.P.

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