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Byju's Answer
Standard XII
Mathematics
nth Term of A.P
If a , b , c ...
Question
If
a
,
b
,
c
are in A.P., then
a
3
+
c
3
−
8
b
3
is equal to
A
−
2
a
b
c
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B
−
6
a
b
c
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C
6
a
b
c
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D
2
a
b
c
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Solution
The correct option is
B
−
6
a
b
c
Given :
a
,
b
,
c
are in A.P., so
2
b
=
a
+
c
Now,
a
3
+
c
3
−
8
b
3
=
a
3
+
c
3
−
(
2
b
)
3
=
a
3
+
c
3
−
(
a
+
c
)
3
=
a
3
+
c
3
−
(
a
3
+
c
3
+
3
a
c
(
a
+
c
)
)
=
−
3
a
c
(
2
b
)
=
−
6
a
b
c
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Standard XII Mathematics
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