# Mathongo is a free app

## Assignment 1 Sequence Series Mathongo

SEQUENCE SERIES

Q1 Consider an infinite geometric series with first term a and common ratio r. If its sum is 4

and the second term is ¾ then find a and r

(a) a = 4/7, r = 3/7 (b) a = 2, r = 3/8

(c) a = 3/2, r = 1/2 (d) a = 3, r = 1/4

Q2 If the sum of the first 2n terms of the AP 2,5, 8, ... is equal to the sum of the first n terms

of the AP 57, 59, 61 ... then find the value of n

(a) 10 (b) 12

(c) 11 (d) 13

Q3 The digit of a positive integer having three digits are in A.P. and their sum is 15. If the

number obtained by reversing the digits is 594 less than the original number, then the number

is

(a) 352 (b) 652

(c) 852 (d) none

( ) ( )

Q4 If 1, log 9 31− x + 2, log 3 4.3x - 1 are in AP then x equals

### (a) log 3 4 (b) 1 - log 3 4

### (c) 1- log 3 4 (d) log 4 3

Q5 Suppose a, b, c are in AP and a 2, b 2, c 2 are in GP. If a **value of a (a) 1/2 2 (b) 1/2 3 1 1 1 1 (c) - (d) - 2 3 2 2**

** www.mathongo.com Master JEE Mains Math 2019 Program SEQUENCE SERIES**

** a1 + a2 + ... a p p2Q6 Let a1… an be terms of AP. If = where p and q are distinct then find a1 + a2 + ... aq q2**

**a6a21 (a) 41 // 11 (b) 7/2 (c) 2/7 (d) 11/41**

**Q7 A person is to count 4500 currency notes. Let a (n) denote the number of notes he countsin the nth minute. If a1 = a2 =… = a10 = 150 and a10, a11 are in AP with common difference -2,**

**then the time taken by him to count all the notes is. (a) 34 minutes (b) 125 minutes (c) 135 minutes (d) 24 minutes**

** 1 2Q8 The maximum value of the sum of the series 20 + 19 + 18 + .... is 3 3 (a) 300 (b) 310 (c) 320 (d) none**

** 1099 1099Q9 Let tn be the nth term of an A.P. If ∑ a 2r = 10100 and r = 1 ∑a r = 1 2r −1 = 1099, then the common**

**difference of A.P. is (a) 1 (b) 10 (c) 9 (d) 1099**

**Q10 In a geometric progression consisting of positive terms, each term equal to the sum of thenext two terms. Then the common ratio of this progression equals:**

** (a) 1 2 ( 1− 5) (b) 1 2 5**

** (c) 5 (d) 1 2 ( 5 −1 )**

** www.mathongo.com Master JEE Mains Math 2019 Program SEQUENCE SERIES**

**Q11 The first two terms of a geometric progression add up to 12. The sum of the third andthe fourth terms is 48. If the terms of the geometric progression are alternately positive andnegative, then the first term is: (a) -4 (b) -12 (c) 12 (d) 4**

**Q12 If a, b, c be three successive terms of a G.P. with common ratio r and a> 0 satisfying therelation c> 4b - 3a, then (a) 1 **

**Q13 A G.P. consists of an even number of terms. If the sum of all the terms is 5 times thesum of the terms occupying odd places, the common ratio will be (a) 2 (b) 3 (c) 4 (d) 5**

**Q14 There are (4n + 1) terms in a certain sequence of which the first (2n + 1) terms from anA.P. of common difference 2 and the last (2n + 1) terms are in G.P. of common ratio 1/2. Ifthe middle terms of both A.P. and G.P. be the same, then mid-term of this sequence is**

** n ⋅ 2n +1 n ⋅ 2n +1 (a) (b) 2n - 1 22n - 1 (c) n ⋅ 2n (d) none**

**Q15 Three numbers form an increasing G.P. if the middle number is doubled, then the newnumbers are in A.P. The common ratio of G.P. is (a) 2 - 3 (b) 2 + 3**

** (c) 3−2 (d) none of these**

** www.mathongo.com Master JEE Mains Math 2019 Program SEQUENCE SERIES**

**Q16 The minimum value of n such that 1 + 3 + 32 + ..... + 3n> 1000 is**

(a) 7 (b) 8

(c) 9 (d) none of these

(a) 7 (b) 8

(c) 9 (d) none of these

a n +1 1 20

Q17 For a sequence a n, a1 = 2 and

at

=. Then,

3

∑a

r = 1

r

is

20 1

(a) [4 + 19 × 3] (b) 3 1 -

2 320

### (c) 2 (1 - 320) (d) none of these

### Q18 If a, b, c, d, e, f are A.M.’s between 2 and 12, then a + b + c + d + e + f is equal to

(a) 14 (b) 42

(c) 84 (d) none of these

Q19 The sum of the squares of three distinct real numbers which are in G.P. is S2. If their

sum is α S, then

(a) 1 <α 2 <3 (b)

1

<α2 <3

3

(c) 1 <α <3 1

(d) <α <1

3

Q20 If a, b, c are three unequal numbers such that a, b, c are in A.P. and b - a, c - b, a are in

G.P., then a: b: c is

(a) 1: 2: 3 (b) 1: 3: 5

(c) 2: 3: 4 (d) 1: 2: 4

www.mathongo.com

**
**

- What's the best way to chop garlic
- How much do you earn
- How do I host landing pages
- How do I install the RHadoop package
- Why Iceland is green and Greenland is icy
- Philadelphia is a sanctuary city
- What is the value of e 5
- How do I take good photos
- What is meant by yard
- What are your favorite wines from Hungary
- How did you finally get disciplined
- How do I stop the Windows 10 update
- Are there narcissistic artists
- Can you describe how good you are
- Will closing liquor stores lower alcohol consumption
- Good guys cheat the most
- How can Paris become a cleaner place
- Why did Walt Disney build Disneyland
- What are derived future contracts
- Why are planets round and galaxies flat
- What is the ranking of computer science students
- Love to watch bollywood movies
- Scalping is a risky daily trading strategy
- What kind of coffee do Indians prefer