CBSE Worksheet for chapter- 5 Arithmetic Progression class 10

Worksheet For class 10

Find CBSE Worksheet for chapter- 5 Arithmetic Progression class 10

CLASS-10

BOARD: CBSE

Mathematic Worksheet - 5

TOPIC: Arithmetic Progression

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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 (a₁) =a+0.d

Second term (a₂) = a+1.d

Third term (a₃) = 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:

1. 3+p/n
2. 3-p/n
3. 3+n/p
4. 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

1. 1:2
2. 2:1
3. 1:3
4. 3:1

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

1. 95^th
2. 100th
3. 102th
4. 101th

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

1. f(n) = an + b, n € N
2. f(n) = k r ⁿ , n € N
3. f (n) = (an+b)krⁿ, n € N
4. 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

1. n²-1
2. (2n-1)²
3. n²
4. n²+1

6) The interior angles of a polygon are in A.P. If the smallest angle be 120^o and the common difference be 5⁰, then the number of sides is.

1. 8
2. 10
3. 9
4. 6

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

1. ab/(-a+b)
2. ab/(2(b-a))
3. 3ab/(2(b-a))
4. 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 =n²p and S_m=m²p,(m p) in an A.P.Prove that S_p=p³
4. The sum of the first n terms of an A.P is given by S_n=3n²-4n.Determine the A.P and its 12^th term.
5. In an A.P, the sum of first n terms is 3n²/2+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 a₁₂ = 65
5. 76
6. -13.-8 and -3
7. First term=2 and Thirteenth term =26
8. 1,-1,-3,-5 …