CLASS-10

BOARD: CBSE

Mathematic Worksheet - 5

TOPIC: Arithmetic Progression

For other **CBSE Worksheet for class 10 Mathematic** check out main page of Entrancei.

**SUMMARY**

**ARITHEMETIC PROGRESSION**

A sequence is called an arithmetic progression (A.P) if the difference of a term and the previous term as always same i.e. d=t_{n+1 }- t_{n }=Constant for all n € N. the constant difference generally denoted by d is called the common difference.

n^{th} term of A.P

Let A.P be a, a+d,a+2d,a+3d,………….

Then First term (a_{1})=a+0.d

Second term (a_{2})=a+1.d

Third term (a_{3})=a+2.d

nth term (a_{n})=a+ (n-1)d

a_{n}=a+(n-1)d is called the nth term.

**SUM OF THE n TERM OF AN A.P**

Let A.P be a, a+d,a+2d,a+3d,………………….a+(n-1)d then

S(n) = (n/2)*[2a+ (n-1)d]

S(n)= (n/2) (a + l) where l is the last term.

**ARITHEMETIC ****MEAN**

Arithmetic Mean A= (a+b)/2

**OBJECTIVE**

**1) p ^{th} term of the series (3-1/n)+(3-2/n)+(3-3/n)+⋯ will be:**

a) 3 +p/n

b)3-p/n

c) 3+n/p

d)3-n/p

**2) If 9 ^{th} term of an A.P be zero then the ratio of its 29^{th} and 19^{th} term is**

a) 1: 2

b) 2:1

c)1:3

d) 3:1

**3) Which term of the sequence 8,13,18………. is 498**

a) 95^{th}

b) 100th

c) 102th

d) 101th

**4) Which of the following sequence is an A.P.?**

a) f(n) = an + b, n € N

b) f(n) = k r ^{n }, n € N

c) f (n) = (an+b)kr^{n}, n€N

d) f (n) = 1/a(n+b/n), n€N

**5) If the nth tern of A.P be (2n-1) then the sum of its first n terms will be**

a ) n^{2}-1

b) (2n-1)^{2}

c) n^{2}

d) n^{2}+1

**6) The interior angles of a polygon are in A.P. If the smallest angle be 120 ^{o} and the common difference be 5^{0}, then the number of sides is.**

a) 8

b) 10

c) 9

d) 6

**7) If the first second and last term of an A.P be a,b,2a respectively then its sum will be:**

a) ab/(-a+b)

b)ab/(2(b-a))

c)3ab/(2(b-a))

d)3ab/(4(b-a))

**SUBJECTIVE**

**1) A student purchased a pen for Rs 100.At the end of the 8 yrs it was valued Rs 20, Assuming the yearly depreciation is a constant amount find the annual depreciation.**

**2) Which term of the sequence 17, 16(1/5),15( 2/5),14( 3/5) … is the first negative term.**

**3) If S _{n }=n^{2}p and S_{m}=m^{2}p,(m p) in an A.P.Prove that S_{p}=p^{3}**

**4) The sum of the first n terms of an A.P is given by S _{n}=3n^{2}-4n.Determine the A.P and its 12^{th} term.**

**5) In an A.P, the sum of first n terms is 3n ^{2}/2+5n/2. Find its 25^{th} term.**

**6) The sum of the 4 ^{th} and 8^{th} term of an A.P is 24 and the sum of the 6^{th} and the 10^{th} term is 44.Find the first three terms of the A.P.**

**7) The sum of the first six term of an arithmetic progression is 42.The ratio of its 10 ^{th} term to its 30^{th} term is 1:3.Calculate the first and the thirteenth term of the A.P.**

**8) In an A.P the sum of its first ten terms is -80 and the sum of its next ten terms is -280. Find the A.P.**

**Answers:**

**Objective: **

1) b

2) b

3) b

4) a

5) c

6) c

7) c

**Subjective: **

1)10

2)23^{rd}

3) ?

4) -1, 5, 11… and a_{12} = 65

5)76

6) -13.-8 and -3

7) First term=2 and Thirteenth term =26

8)1,-1,-3,-5 …