# Progression Questions

Know here how to solve different types of Arithmetic Progression Questions for various competitive and entrance examination such as SSC CGL/Railway/CAT and many others. Important and selective Progression Questions are available here and by solving these questions, you will be able to know the tricks used behind it.

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 Arithmetic Progression:Arithmetic Progression is a sequence in which a constant is added to each term to get next term in the sequence. The constant term is called as the common difference of the A.P.Suppose, a1,a2,a3,………an are the terms of an A.P.Then, a2 = a1+d, a3 = a2+d , where a1 is the 1st term & d is the common difference which is constant for an Arithmetic Progression.For example,2, 5, 8, 11……… is an A.P with common difference 3.3, 9, 15, 20…… is not an A.P because a4–a3 = 5 which is not equal to (a2–a1).Progression Formula:nth term of an A.P : an = a+(n–1)dSum of AP:  Sum of n terms of an A.P = n/2[2a + (n−1) d]Arithmetic Progression Formula:  n [2a + (n–1) d]/2 = n [a+ a + (n–1) d]/2 =n [a + an]/2

Once you clear up the conceptual part, then Arithmetic Progression Questions and Answers will be solved within a minute at examination time.

## Progression Questions

Answers for these questions are available at the end.

Question 1) The 5th term of an AP is 17/6 and the 9th term is 25/6. What is the 12th term?

1. 29/6
2. 31/6
3. 33/6
4. 34/6

Question 2) The sum of the first 3 terms in an AP is 51 and that of the last 3 is 99. If the AP has 11 terms, what is the arithmetic mean of the middle 3 terms?

1. 17
2. 19
3. 21
4. 25

Question 3) The first term of an AP is 3 and the last term is 17. If the sum of all terms is 150, what is the 5th term?

1. 5
2. 7
3. 9
4. 11

Question 4) In an AP, the ratio of the 2nd term to the 6th term is 2/5. If the 8th term is 26, what is the 10th term?

1. 28
2. 29
3. 32
4. 33

Question 5) The sum of three numbers in Arithmetic Progression is 72 and their product is 11880. What are the numbers?

1. 21, 24, 27
2. 12, 24, 36
3. 18, 24, 30
4. 15, 24, 33

Question 6) In an AP, the sum of the first 3 terms is – 60 and that of the last 3 are 84. If there are 15 terms, what is the sum of the middle 3 terms?

1. 8
2. 12
3. 16
4. 24

Question 7) The sum of the first six terms of an AP is 48 and the common difference is 2. What is the 4th term?

1. 6
2. 7
3. 9
4. 10

Question 8) In an AP, the sum of the first 3 terms is -36 and that of the last 3 is 27. If there are 10 terms, what are the 1 st term and the common difference respectively?

1. 15, 3
2. -15, 3
3. 15, -3
4. -15, -3

Question 9) The sum of three numbers in an Arithmetic Progression is 45 and their product is 3000. What are the three numbers?

1. 5, 15, 25
2. 12, 15, 18
3. 10, 15, 20
4. -10, -15, -20

Solve Here: Permutation Combination Questions

Question 10) In an AP, the ratio of the 7th term to the 10th term is -1. If the 16th term is -15, what is the 3rd term?

1. 11
2. 13
3. -11
4. -13

Question 11) The first term of an AP is 10 and the last term is 28. If the sum of all terms is 190, what is the common difference?

1. 5
2. 3
3. 1
4. 2

Question 12) The sum of the first 3 terms in an AP is 6 and that of the last 3 is 16. If the AP has 13 terms, what is the sum of the middle three terms?

1. 7
2. 9
3. 11
4. 13

Question 13) The first term of an Arithmetic Progression is 15 and the last term is 85. If the sum of all terms is 750, what is the 6th term?

1. 30
2. 40
3. 45
4. 55

Question 14) In an AP, the ratio of the 2nd term to the 7th term is 1/3. If the 5th term is 11, what is the 15th term?

1. 28
2. 31
3. 33
4. 36

Question 15) An Arithmetic Progression has 23 terms, the sum of the middle three terms of this arithmetic progression is 720, and the sum of the last three terms of this Arithmetic Progression is 1320. What is the 18th term of this Arithmetic Progression?

1. 240
2. 360
3. 340
4. 440

Question 16) The 6th term of an AP is 6 and the 16th term is 14. What is the 27th term?

1. 106/5
2. 22/5
3. 118/5
4. 114/5

Question 17) There is a set of four numbers p, q, r and s respectively in such a manner that first three are in G.P. and the last three are in A.P. with a difference of 6. If the first and the fourth numbers are the same, find the value of p.

1. 8
2. 2
3. –4
4. –24

Question 18) In an AP of 21 terms, the sum of the first 3 terms is – 33 and that of the middle 3 is 75. What is the sum of the AP?

1. -955
2. -1155
3. 525
4. 715

Question 19) The first and third terms of an A.P. {A1} are A1 = a and A3 = b, and a1 = a and a5 = b respectively be the first and fifth terms of another A.P. {a1}. Find the ratio of An+1 and a2n+1.

1. 2
2. 4
3. 1
4. b/a

Get Here Important: Mensuration Questions and Answers

Question 20) The 7th term of an AP is -39/12 and the 15th term is -103/12. What is the 27th term?

1. -187/12
2. -191/12
3. -199/12
4. -205/12