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Arithmetic progression (AP) is a sequence of numbers in which each term after the first is found by adding a constant, called the common difference, to the previous term. For example, the sequence 3,6,9,12... is an arithmetic progression with a common difference of 3. The nth term of an arithmetic progression can be found using the formula: a + (n-1)d, where a is the first term and d is the common difference. The sum of an arithmetic progression can be found using the formula: (n/2)(2a + (n-1)d), where n is the number of terms in the progression.

Sample Test Paper

Que 1--

Find the first term and common difference, nth term and the 25th term for the series

-4,-5/2,-1,1/2,2............

Que. 2--

If nth term of arithmetic progression is.

Tn = 4n-7

find the 20th term of the series

Que 3--

Which term of the arithmetic progression

4,9,14,19........

is 79

Que 4---

How many terms are there in the arithmetic progression

9,13,17,21...............97

Que 5 ----

Which term of arithmetic progression is first negative term

45,42,39,36............

Que 6 ----

Find 8th term from the end of the arithmetic progression

4,9,14...................254

Que 7 ---

If (k- 3) (2k+1) and (4k+3) are three terms of arithmetic progression find the value of k

Que 8 ---

Find three numbers which are in AP whose sum is 15 and product is 80

Que 9 ---

Find the sum of the following series

a) 3,8,13,18............... upto 15 terms

b) 9,7,5,3 ..............upto 14 terms

c) 33,37,41,..........101

Que 10 ---

Find sum of all two digit numbers which are divisible by 3

Que 11---

The 4th term of an AP is 22 and 15th term of an AP is 66. Find the sum of series upto 8 terms

Que 12 ---

A sum of rupees 2800 is to be used to award four prizes if each price after the first is 200 less than the preceding price find the value of each prize

Que 13-- How many three digit numbers are divisible by 5

Thu Jan 12, 2023

Que 1

If the mth term of an AP is 1/n and nth term is 1/m then sum of mn terms is

a) 1/2(m n-1)

b) 1/2(mn+1)

c) mn+1

d) mn-1

Ans (b)

Que 2

The ratios of sums of m and n terms of an AP is m^2:n^2 then the ratio of mth term and nth term is

a) (2m+1):(2n+1)

b) m:n

c) ( 2m-1):(2n-1)

d) none of these

Ans ( c)

Que 3

The sum of the series 1+ 4/5 +7/5^2+10/5^3.....

a) 7/16

b) 5/16

c) 105/64

d) 35/16

Ans ( d)

Que 4

If the roots of the equation

x^3-12x^2+39x-28=0 are in AP then their common difference will be

a) 1

b) 2

c) 3

d) 4

Ans (c)

Que 5

If AM of two numbers is twice of their GM then ratio of greatest number to smallest number is

a) 7-4√3

b) 7+4√3

c) 21

d) 5

Ans (b)

Que 6

Let two numbers have arithmetic mean 9 and geometric mean 4 then these numbers are the roots of the quadratic equation

a) x^2-18x-16=0

b) x^2-18x+16=0

c) x^2+18x-16=0

d)x^2+18x+16=0

Que 7-

The sum of all odd numbers between 1 and 1000 which are divisible by 3

a) 83367b) 90000

c) 93660

d) none of these

Ans (a)

The sum of the series 1.2.3 + 2.3.4+ 3.4.5 ..to n terms is

a) n(n+1)(n+2)

.b) (n+1)(n+2)(n+3)

c) 1/4 n(n+1)(n+2)(n+3)

d) 1/4 (n+1)(n+2)(n+3)

Ans (c)

.b) (n+1)(n+2)(n+3)

c) 1/4 n(n+1)(n+2)(n+3)

d) 1/4 (n+1)(n+2)(n+3)

Ans (c)

The sum of series 6+66+666+6666+... upto n terms a) (10^n -1 -9 n+10)/81

b) 2(10^n- 1-9n+10)/27c) 2(10^n -9 n+10)/27

d) none of these

b) 2(f- d)

c) 2(d- c)

d) d - c

Ans (c)

Arithmetic Progression Definition.

Sonika Agarwal

Arithmetic progression

An arithmetic progression (AP) is a sequence of numbers in which each term after the first is found by adding a constant, called the common difference, to the previous term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic progression with a common difference of 3. The nth term of an arithmetic progression can be found using the formula: a + (n-1)d, where a is the first term and d is the common difference. The sum of an arithmetic progression can be found using the formula: (n/2)(2a + (n-1)d), where n is the number of terms in the progression.

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