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Byju's Answer
Standard XII
Mathematics
nth Term of A.P
x1, x2, x3, a...
Question
x
1
,
x
2
,
x
3
, ________ are in A.P. If
x
1
+
x
7
+
x
10
=
−
6
and
x
3
+
x
8
+
x
12
=
−
11
, then
x
3
+
x
8
+
x
22
=
__________.
A
−
21
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B
−
15
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C
−
18
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D
−
31
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Solution
The correct option is
A
−
21
Let the first term be
a
and common difference be
d
x
1
+
x
7
+
x
10
=
−
6
⇒
(
a
)
+
(
a
+
6
d
)
+
(
a
+
9
d
)
=
−
6
⇒
3
a
+
15
d
=
−
6
→
eqn
(
1
)
x
3
+
x
8
+
x
12
=
−
11
⇒
(
a
+
2
d
)
+
(
a
+
7
d
)
+
(
a
+
11
d
)
=
−
11
⇒
3
a
+
20
d
=
−
11
→
eqn
(
2
)
Solving eqn (1) and (2), we get
a
=
3
and
d
=
−
1
Now,
x
3
+
x
8
+
x
22
=
3
a
+
30
d
=
−
21
So, option (A)
Suggest Corrections
0
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Q.
x
1
,
x
2
,
x
3
,
.
.
.
are in A.P. If
x
1
+
x
7
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x
10
=
−
6
and
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+
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=
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, then the value of
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x
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<
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<
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, then the median of
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Q.
If the median of the observations x
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, x
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, x
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, x
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, x
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, x
8
is m, then the median of the observations x
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, x
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, x
5
, x
6
(where x
1
< x
2
< x
3
< x
4
< x
5
< x
6
< x
7
< x
8
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Q.
If
x
1
and
x
2
are the roots of the equation
e
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, then
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Let
x
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x
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1
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−
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)
2
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2
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Standard XII Mathematics
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