AHLCON PUBLIC SCHOOL
Class : XI (2014-2015)
ASSIGNMENT- 9
TOPIC – SEQUENCE AND SERIES
Q.1
If pth , qth & rth terms of an A.P are a, b, c respectively, then show that:
i)
ii)
a (q – r) + b ( r – p) + c ( p – q) = 0
(a – b)r + (b – c) p + (c – a ) q = 0
1
1
& nth term be
, then show that its (mn)th term is 1.
n
m
Q.2
If the mth term of an A.P be
Q.3
Determine the number of terms in the A.P. 3, 7, 11, ---------, 4.7. Also find its 20th term from the
end.
Q.4
Find four numbers in A.P. hose sum is 20 & the sum of whose squares is 120.
Q.5
Find the sum of first 24 terms of the A.P. a, a2, a3, -----, if it is known that
a1  a5  a10  a15  a20  a24  225.
Q.6
If in an A.P. the sum of m terms is equal to n & the sum of n terms is equal to m, then prove that
the sum of (m + n) terms is – (m + n)
Q.7
The ratio of the sum of n terms of two AP’s is (7n + 1) : (4n + 27). Find the ratio of their m th
terms.
Q.8
If a, b, c, are in AP, Prove that b  c   a 2 , c  a   b 2 , a  b   c 2 are also in A.P.
Q.9
If n arithmetic means are inserted between 20 & 80 such that the ratio of first mean to the last
mean is 1:3, then find value of n.
Q.10
solve for x,the equation 2+7+12+17+………..+x=156
Q.11
Three numbers are in G.P whose sum is 70. If the extremes be each multiplied by 4 & the means
by 5, they will be in A.P. Find the numbers.
Q.12
In an increasing G.P, the sum of the first & the last term is 66, the product of the second & the
second last is 128 & the sum of the terms is 126. How many terms are there in the progression.
Q.13
If mth, nth & pth terms of a G.P form 3 consecutive terms of a G.P prove that m, n & p
form three consecutive sequence.
Q.14
Find two positive numbers whose difference is 12 & whose A.P exceeds G.M. by 2.
Q.15
Find the sum of n terms of the series whose nthterm is (2n2 – 3n + 5).
Q.16
Find the sum to n terms of the series

2
 
i)
ii)
3 + 15 + 35 + 63 + ------------------5 + 7 + 13 + 31 + 85 + --------------.
iii)
1
1
1


 ........
2  5 5  8 8 11
1 22  2  32  3  42  .........
1 2  4  2  3 7  3 4 10  ........
iv)
v)
2
 
2

Q.17
Find three numbers in GP whose sum is 52 & the sum of whose products in pairs is 624.
Q.18
Find three numbers in G.P whose sum is 13 & the sum of whose squares is 91.
Q.19
If a, b, c, d are in G.P prove that
b  c 2  c  a 2  d  b 2  a  d 2
Q.20
If the sum of m terms of an AP be n & the sum of n terms be m, show that the sum of
(m + n) terms is -(m + n).