# Arithmetic Progressions in Mathematics

An arithmetic progression is a list of numbers in which each term  isobtained  by  adding  a  fixed  number  to  the  preceding  term  except  the  firstterm. This fixed numberis called the common difference of the AP.  Remember that it  can  be  positive,  negative  or  zero.

For examples of AP Let the heights ( in cm ) of some students of a school standing in a queue in themorning assembly are 147 , 148, 149, . . ., 157.

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### Related FAQs

Q. Find the 20th term from the last term of the A.P. : 3, 8, 13, …, 253.

Ans: Given A.P. series is 3, 8, 13, …, 253 Here, first term is a = 3 And common difference b/w terms is d = 8 - 3 = 5 Here last term is 253, So first of all we find out total number terms in the ... read more

Q. The value of x for which 2x, (x+10) and (3x+2) are the three consecutive terms of an AP, is

Ans: Since 2x, (x+10) and (3x+2) are in AP we obtain, (x + 10) − 2x = (3x + 2) − (x + 10) -x + 10 = 2x -8 -x - 2x = -8 -10 -3x = -18 x = 6 Hence answer is x = 6 ... read more

Q. The first term of AP is p and the common difference is q , then its 10th term is

Ans: Here first term a = p and common difference d = q As a10 = a + ( 10 − 1 )d a10 = p + 9q So 10th term is (p + 9q)... read more

Q. In an AP, if d = − 4 , n = 7 and an = 4 , then a is equal to

Ans: As an = a + ( n − 1 ) d According to given values 4 = a + (7 − 1) (− 4) 4 = a + 6 (− 4) 4 + 24 = a  a = 28 , Hence first term a is 28... read more

Q. What is the common difference of an AP in which a18 − a14 = 32 ?

Ans: As it is given that a18 − a14 = 32 (a + (18-1)d) - (a + (14-1)d) = 32 a + 17d - a - 13d = 32 4d = 32 d = 8 Hence required common difference is 8.... read more

Q. Second term of an arithmetic sequence is 5 and fifth term is 2 The common difference will be

Ans: As we know that  an = a + ( n − 1 ) d It is given that Second term of an arithmetic sequence is 5  So   a2 = 5 Fifth term of an arithmetic sequence is 2  So  a5 = 2 ... read more

Q. The second and eighth term of an arithmetic progression are 17 and 1 respectively what is the 14th Term

Ans: As an = a + ( n − 1 ) d It is given that a2 = 17 a8 = 1 As a2 = 17 a + (2 - 1)d = 17 a + d = 17 a = 17 - d   -------------------------(1) As a8 = 1 a + (8 - 1)d = 1 a + 7... read more

Q. The nth term of any arithmetic progression in 4n-3 find the 15th term

Ans: For the AP sequence, the nth term can be given by   an = a + (n-1)d  -------------------(1) It is given that an = 4n-3 an = 4 - 4 + 4n - 3 an = 4 - 3 + 4n - 4 an = 1 + (n -1)4 ... read more

Q. The nth term of a sequence is n^2+ 5. Find the first three terms of this sequence.

Ans: Here Tn = n2 + 5 Now first three terms are T1 = 12 + 5  = 1 + 5= 6 T2 = 22 + 5 = 4 + 5 = 9 T3 = 32 + 5 = 9 + 5 = 14 Hence first three terms are 6, 9, 14... read more