# JEE Main > Progressions

Explore popular questions from Progressions for JEE Main. This collection covers Progressions previous year JEE Main questions hand picked by experienced teachers.

Physics
Chemistry
Mathematics
Q 1.

Correct4

Incorrect-1

In a certain A.P., 5 times the 5th term is equal to 8 times the 8th term, then its 13th term is

0

B

-1

C

-12

D

-13

##### Explanation

We have
Let a and d be the first term and common difference respectively

, i.e. .
Hence 13th term = 0

Q 2.

Correct4

Incorrect-1

If 7th and 13th term of an A.P. be 34 and 64 respectively, then its 18th term is

A

87

B

88

89

D

90

##### Explanation

Let a be the first term and d be the common difference of the given A.P., then

From
(i) and
(ii), d = 5, a = 4

Trick:

Q 3.

Correct4

Incorrect-1

If is an arithmetic sequence, then equals

A

1

B

-1

0

D

None of these

##### Explanation

Let a be the first term and d the common difference. Then

Q 4.

Correct4

Incorrect-1

The nth term of the series 3 + 10 + 17 + .. and 63 + 65 + 67 +...... are equal, then the value of n is

A

11

B

12

13

D

15

##### Explanation

nth term of 1st series
nth term of 2nd series
we have, ⇒ n = 13

Q 5.

Correct4

Incorrect-1

7th term of an A.P. is 40, then the sum of first 13 terms is

A

53

520

C

1040

D

2080

##### Explanation

Q 6.

Correct4

Incorrect-1

The first term of an A.P. is 2 and common difference is 4. The sum of its 40 terms will be

3200

B

1600

C

200

D

2800

##### Explanation

Q 7.

Correct4

Incorrect-1

The sum of the first and third term of an A.P. is 12 and the product of first and second term is 24, the first term is

A

1

B

8

4

D

6

##### Explanation

Let be an A.P.
. Also,

First term

Q 8.

Correct4

Incorrect-1

If denotes the sum of the first r terms of an A.P., then is equal to

A

2r - 1

2r + 1

C

4r + 1

D

2r + 3

##### Explanation

Q 9.

Correct4

Incorrect-1

If the sum of the first 2n terms of 2, 5, 8...... is equal to the sum of the first n terms of 57, 59, 61., then n is equal to

A

10

B

12

11

D

13

##### Explanation

We have,

Q 10.

Correct4

Incorrect-1

If the sum of the 10 terms of an A.P. is 4 times to the sum of its 5 terms, then the ratio of first term and common difference is

1 : 2

B

2 : 1

C

2 : 3

D

3 : 2

##### Explanation

Let a be the first term and d the common difference
Then,
, a : d = 1 : 2

Q 11.

Correct4

Incorrect-1

150 workers were engaged to finish a piece of work in a certain number of days. 4 workers dropped the second day, 4 more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

A

15

B

20

25

D

30

##### Explanation

Let the work was to be finished in x days.
Work of 1 worker in a day
Now the work will be finished in (x + 8) days.
Work done = Sum of the fraction of work done
to
(x + 8) terms

,
Hence work completed in 25 days.

Q 12.

Correct4

Incorrect-1

If the sum of first p terms, first q terms and first r terms of an A.P. be x, y and z respectively, then is

0

B

2

C

pqr

D

##### Explanation

We have a, the first term and d, the common difference,
Similarly, and

Q 13.

Correct4

Incorrect-1

The sum of all odd numbers of two digits is

2475

B

2530

C

4905

D

5049

##### Explanation

Required sum,
Let the number of odd terms be n, then

Q 14.

Correct4

Incorrect-1

If sum of n terms of an A.P. is and , then m =

A

26

27

C

28

D

None of these

##### Explanation

Q 15.

Correct4

Incorrect-1

The sum of n terms of the series is

A

B

C

##### Explanation

Q 16.

Correct4

Incorrect-1

If are in A.P., then is

A

B

C

##### Explanation

As are in A.P., i.e.
(say)

Q 17.

Correct4

Incorrect-1

If the pth, qth and rth term of a G.P. are a, b, c respectively, then is equal to

A

0

1

C

abc

D

pqr

##### Explanation

Let be a G.P.

Now,

Q 18.

Correct4

Incorrect-1

Let be the nth term of the G.P. of positive numbers. Let and , such that α≠β, then the common ratio is

B

C

D

##### Explanation

Let x be the first term and y, the common ratio of the G.P.
Then,and
. Thus, common ratio

Q 19.

Correct4

Incorrect-1

The sum of first two terms of a G.P. is 1 and every term of this series is twice of its previous term, then the first term will be

A

C

D

##### Explanation

We have, common ratio r = 2;
Let a be the first term, then

Q 20.

Correct4

Incorrect-1

The first term of an infinite geometric progression is x and its sum is 5. Then

A

C

D

##### Explanation

According to the given conditions, , r being the
common ratio ⇒
Now, |r|< 1 i.e. i.e. ,

Q 21.

Correct4

Incorrect-1

is

A

e + 1

e - 1

C

1 - e

D

e

##### Explanation

.

Q 22.

Correct4

Incorrect-1

The value of .234 is

B

C

D

##### Explanation

Q 23.

Correct4

Incorrect-1

If a, b, c are in A.P. and |a|, |b|, |c| < 1, and , , Then x, y, z shall be in

A

A.P.

B

G.P.

H.P.

D

None of these

##### Explanation

Now, a, b, c are in A.P.
⇒ 1 - a, 1 - b, 1 - c are in A.P.
are in H.P.
Therefore x, y, z are in H.P.

Q 24.

Correct4

Incorrect-1

The G.M. of the numbers is

A

C

D

##### Explanation

G.M. of

Q 25.

Correct4

Incorrect-1

If a, b, care in A.P. b - a, c - b and a are in G.P., then a : b : c is

1 : 2 : 3

B

1 : 3 : 5

C

2 : 3 : 4

D

1 : 2 : 4

##### Explanation

Given, a, b, c are in A.P. ⇒ 2b = a + c
b - a, c - b, a are in G.P. So

[∵ b ≠ a]
Put in 2b = a + c, we get c = 3a. Therefore a : b : c = 1 : 2 : 3