Pervious year question
Q.2
find the next five term of a1 = ½ ,
a2=-1 , an+2 =anan+1.
?
Q.3.Show
that the sequence defined an=2 n2+1 is not an A.P.
Q.4
show that sequence
is the A.P find its nth term.
Q.5
which term of the sequence 45,41,37,33… is first negative term?
Q.6 Is
302 a term of the A.P 3,8,13… ?
Q.7. If
the mth term of an A.P be
and nth term be
,then
show that its (mn)th term is 1.
Q.8. If
(m+1)th term of an A.P is twice the (n+1)th term .prove that (3m+1)th term is
twice the (m+n-1)th term.
Q.9 If
pth,qth and rth terms of an A.P are a,b& c respectively . show that
a(q-r)+b(r-p)+c(p-q) =0.
Q.10 If
the nth term of a progression be a linear expression then prove that this
progression is an A.P.
Q.11 Find
three number in an A.P whose sum is 18 and whose product in 192.
Q.12 Find
four number in an A.P whose sum is 28 and sum of whose square is 216.
Q.13 The
sum of n terms of an A.P is 3n2+4n.find the nth term hence, find the
A.P.
Q.14
The digit of a positive number having three digit is A.P and their sum is 15.
The number obtained by reversing the digits is 594 less than the original
number. Find the number.
Q.15
If the mth term of an A.P Is
and the nth term is
.show that the sum of mnth term is
.
Q.16
If the sum of m terms of an A.P is the same as the sum of its n term ,show that
the sum of its (m+n)term is zero.
Q.17
If in an A.P the sum of m terms is equal to n and the sum of n terms is equal
to m. then prove that the sum of (m+n)term is –(m+n).
Q.18
In an A.P the pth term is a and qth term is b,then show that the sum of the first (p+q)term is
.
Q.19
The sum of n,2n,and 3n term of an A.P are s1,s2 and s3
resp. prove that s3=3(s2-s1).
Q.20
The sum of the first p,q,r terms of an A.P are a,b,c respectively show that
.
Q.21
The sum of n term of two A.P are in the ratio 7n+1:4n+27. Find the ratio of
their 11th terms.
Q.22
The ratio of the sums of m and n term of an A.P is m2:n2.
show
that the ratio of mth and nth term is (2m-1):(2n-1).
Q.23
Find the sum of n term
(i)(x+y)2,x2+y2,(x-y)2...to
10term
(ii)
... to
27term
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