CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 9 – Sequences and Series Maths
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Question 16:
If
1 1 1 1 1 1
a , b ,
c
b c c a a b
Solution 16:
It is given that a
are in A.P., prove that
1 1 1 1 1 1
a , b ,
c
b c c a a b
1 1 1 1 1 1 1 1
b a c b
c a b c a b c a
b a c a b c c a b b a c
ac bc ab ac
2 2 2 2 2 2 2 2
b a b c a b a c c a c b b a b c
abc
abc
2 2 2 2 2 2 2 2
b a a b b c a c c a b a c b b c
2 2 2 2
ab b a c b a a c b bc c b
are in A.P.
ab b a c b a b a a c b c b bc c b
b aab cb ca c bac ab bc
ba c b
Thus, and c are in A.P.
ab ,
abc , ,
are in A.P.
Question 17:
If
a, b, c,
d
Solution 17:
It is given that
b
c
2
ad
2
ac
bd
bc
are in G.P., prove that
abc , ,
...... 1
........ 2
...... 3
and d are in G.P.
a b , b c , c d
n n n n n n
It has to be proved that
n n 2
n n n n
b c a b , c d
Consider L.H.S.
2 2 2
b c b 2b c c
n n n n n n
a b , b c , c d
n n n n n n
are in G.P. i.e.,
are in G.P.
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