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Byju's Answer
Standard XII
Mathematics
nth Term of A.P
State True or...
Question
State True or False. If a, b, c are in A.P., then
b
+
c
,
c
+
a
,
a
+
b
are also in A.P.
A
True
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B
False
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Solution
The correct option is
A
True
We have,
a
,
b
,
c
are in
A
.
P
So,
2
b
=
a
+
c
.
.
.
.
.
.
.
.
.
.
.
.
(
1
)
2
b
+
c
+
a
=
2
a
+
2
c
b
+
b
+
c
+
a
=
c
+
a
+
c
+
a
b
+
c
+
a
+
b
=
2
(
c
+
a
)
2
(
c
+
a
)
=
b
+
c
+
a
+
b
So,
b
+
c
,
c
+
a
,
a
+
b
are in
A
.
P
Hence, this is the answer. Hence the answer is True.
Suggest Corrections
0
Similar questions
Q.
If
a
2
,
b
2
,
c
2
are in A.P. then the following are also in A.P. True or False? If true write 1 otherwise write 0
a
b
+
c
,
b
c
+
a
,
c
a
+
b
.
Q.
If
b
+
c
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+
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+
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are in A.P then Prove that
a
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b
,
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are also in A.P.
Q.
If
b
+
c
−
a
a
,
c
+
a
−
b
b
,
a
+
b
−
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c
are in A.P., then
1
a
,
1
b
,
1
c
are also in A.P.
Q.
If
a
,
b
,
c
are in A.P., then show that:
(i)
a
2
(
b
+
c
)
,
b
2
(
c
+
a
)
,
c
2
(
a
+
b
)
are also in A.P.
(ii)
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+
c
−
a
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+
a
−
b
,
a
+
b
−
c
are in A.P.
Q.
If a, b, c are in A.P., then show that the following are also in A.P.
b
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Standard XII Mathematics
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