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 (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:
2) If 9^{th} term of an A.P be zero then the ratio of its 29^{th} and 19^{th} term is
3) Which term of the sequence 8,13,18………. is 498
4) Which of the following sequence is an A.P.?
5) If the nth tern of A.P be (2n-1) then the sum of its first n terms will be
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.
7) If the first second and last term of an A.P be a,b,2a respectively then its sum will be:
SUBJECTIVE
Answers:
Objective:
Subjective: