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
For other CBSE Worksheet for class 10 Mathematic check out main page of Physics Wallah.
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:
- 3+p/n
- 3-p/n
- 3+n/p
- 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
- 1:2
- 2:1
- 1:3
- 3:1
3) Which term of the sequence 8,13,18………. is 498
- 95^{th}
- 100th
- 102th
- 101th
4) Which of the following sequence is an A.P.?
- f(n) = an + b, n € N
- f(n) = k r ^{n }, n € N
- f (n) = (an+b)kr^{n}, n € N
- 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
- n^{2}-1
- (2n-1)^{2}
- n^{2}
- 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.
- 8
- 10
- 9
- 6
7) If the first second and last term of an A.P be a,b,2a respectively then its sum will be:
- ab/(-a+b)
- ab/(2(b-a))
- 3ab/(2(b-a))
- 3ab/(4(b-a))
SUBJECTIVE
- 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.
- Which term of the sequence 17, 16(1/5),15( 2/5),14( 3/5) … is the first negative term.
- If S_{n }=n^{2}p and S_{m}=m^{2}p,(m p) in an A.P.Prove that S_{p}=p^{3}
- 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.
- In an A.P, the sum of first n terms is 3n^{2}/2+5n/2. Find its 25^{th} term.
- 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.
- 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.
- 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:
- b
- b
- b
- a
- c
- c
- c
Subjective:
- 10
- 23^{rd}
- ?
- -1, 5, 11… and a_{12} = 65
- 76
- -13.-8 and -3
- First term=2 and Thirteenth term =26
- 1,-1,-3,-5 …
Related Link
- Class 10 Physics Notes
- Class 10 Chemistry Notes
- Class 10 Biology Notes
- Class 10 Maths Notes
- Chapter Wise Quiz Class 10 Physics
- Chapter Wise Quiz Class 10 Chemistry
- Chapter Wise Quiz Class 10 Biology
- Chapter Wise Quiz Class 10 Maths
- Previous year Board Papers
- Sample Papers Maths Class 10
- Sample Papers Science Class 10
- NCERT Maths Solutions Class-10