1.Arthemetic sequence:
A sequence is said to be and arthematic sequence( or arthematic progression) if the difference between a term and its preceding term is equal or constant throught the whole sequence.
Eg. i)3,6,9,12,15,...................
ii)20,10,0,-10,-20,..............
2.Geometric Sequences
A sequence of number is said to be a geometric sequence if the ratio of a term and its preceding term is constant throught the whole sequence.
Eg. i) 2 ,6,18,54,......... ii)16,8,4,2,..........
Some important formula
i) nth term(tn)=a+(n-1)d
ii)common difference(d)=succeeding term-preceding term
iii)Last term(L)=a+(n-1)d
iv)If m be the arthematic mean between a and b ,then m=(a+b)/2
v)If m1,m2,m3,.........mn be arthematic means between a and b then
m1=a+d
m2=a+2d
m3=a+3d
................
.................
mn=a+nd
where,d=(b-a)/(n+1)
vi)The sum of first n terms of arthematic series
Sn=(n/2){2a+(n-1)d}
vii)If last term is given
Sn=n/2(a+l)
viii)The sum of first n natural numbers
Sn=n(n+1)/2
ix)The sum of first n odd natural numbers
Sn=n^2 x)The sum of first n natural numbers
Sn=n(n+1)
xi)The sum of first n naturals numbers
Sn={n(n+1)(2n+1)}/6
xii)The sum of first n cube natural numbers
Sn={n(n+1)/2}^2
B.Geometric series
i) nth term(tn)=a.r^(n-1)
ii)Last term (L)=a.r^(n-1)
iii)Common ratio(r)=succeding term/preceeding term
iv)if G be geometric mean between a and b then G=±√(ab)
v)If.G1,G2,G3,..............Gn be the geometric mean between a and b then
G1=a.r
G2=a.r^2
G3=a.r^3
...............
................
Gn=a.r^n
Where r=(b/a)^(1/(n+1))
vi)sum of first n terms(Sn)=a(r^n-1)/(r-1)
vii)if last term L is given than
Sn=(L.r-1)/(r-1)
viii)if |r|≤1,then sum.og infinite series S∞=a/(1-r)
SOME IMPORTANT QUESTIONS
i) If x+2,3x and 4x+1 are in A.P ,find value of x. Ans.3
ii)Find 23rd term of 7,5,3,1,-1.-3,........ Ans.-37
iii)Is 301 a term of seqience 5,11,17,23,........? Ans.no
iv)Find the common difference of A.S whose first term is 3 and 15th term is 73? Ans.5
v)8th term of a sequence is 6 and 10th term is -2,find 9th term . Ans.2
vi)The fifth and 13th terms of an A.P are 5 and -3 respectively,findthis A.P?
vii.The sum of 4th and 8th terms of an A.P is 24 and the sum of 6th and 10th terms is 34.find four terms of A.P
viii)Find thres number in A.P whose sum is 15 and product is 80.
ix)There are n A.M's between 3 and 17 .the ratio of last mean to the first mean is 3:1,find value of n.
x)First and second terms of geometrical sequence are 32 and 8 respectively .what will be the 8th term? Ans.254
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