Mathematic Worksheet - 5
TOPIC: Arithmetic Progression
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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=tn+1 - tn =Constant for all n € N. the constant difference generally denoted by d is called the common difference.
nth 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 (an)=a+ (n-1)d
an=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.
Arithmetic Mean A= (a+b)/2
1) pth term of the series (3-1/n)+(3-2/n)+(3-3/n)+⋯ will be:
a) 3 +p/n
2) If 9th term of an A.P be zero then the ratio of its 29th and 19th term is
a) 1: 2
3) Which term of the sequence 8,13,18………. is 498
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)krn, 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 ) n2-1
6) The interior angles of a polygon are in A.P. If the smallest angle be 120o and the common difference be 50, 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:
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 Sn =n2p and Sm=m2p,(m p) in an A.P.Prove that Sp=p3
4) The sum of the first n terms of an A.P is given by Sn=3n2-4n.Determine the A.P and its 12th term.
5) In an A.P, the sum of first n terms is 3n2/2+5n/2. Find its 25th term.
6) The sum of the 4th and 8th term of an A.P is 24 and the sum of the 6th and the 10th 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 10th term to its 30th 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.
4) -1, 5, 11… and a12 = 65
6) -13.-8 and -3
7) First term=2 and Thirteenth term =26