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Byju's Answer
Standard XII
Mathematics
Relation between AM,GM,HM for 2 Numbers
a 1, a 2, a 3...
Question
a1,a2,a3,a4,a5 are the first five terms of an ap such that a1+a3+a5= -12 & a1a2a3=8 find the first term and common difference
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Solution
Let d be the common difference .
A1+ (A1+2d) + (A1+4d) = -12 and
A1*(A1+2d) *(A1+4d) = 8 and
solve equations for A1 and d
Now A2+A4+A6 = (A1+d) + (A1+3d) + (A1+5d).
Substitute values for A1 and d found in previous step.
Shorter method
Let d be the common difference .
(A3-2d)+ A3 + (A3+2d) = -12 and
A3 = -4
(A3-2d)* (A3-d) *(A3) = 8
Solve for d
Now A2+A4+A6 = (A3-d) + (A3+d) + (A3+2d).
Substitute values for A3 and d found in previous step.
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Q.
a
1
,
a
2
,
a
3
,
a
4
,
a
5
are first five terms of an A.P. such that
a
1
+
a
3
+
a
5
=
−
12
and
a
1
a
2
a
3
=
8
. Find the first term and the common difference.
Q.
If
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a
2
,
a
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,
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a
n
are first n terms of an A.P. with first term
a
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=
0
and common difference
d
≠
0
Then value of
a
3
−
a
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a
2
+
a
4
−
a
2
a
3
+
a
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−
a
2
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.
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.
.
.
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.
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a
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−
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n
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is
Q.
If
a
,
a
2
,
a
3
,
.
.
.
.
,
a
n
are first
n
terms of an AP with first term
a
=
0
and common difference
d
≠
0
Then value of
a
3
−
a
2
a
2
+
a
4
−
a
2
a
3
+
a
5
−
a
2
a
4
.
.
.
.
+
a
n
−
a
2
a
n
−
1
is
Q.
If for an A.P.
a
1
,
a
2
,
a
3
.
.
.
.
.
.
.
.
.
a
n
,
a
1
+
a
3
+
a
5
=
−
12
and
a
1
a
2
a
3
=
8
then the value of
a
2
+
a
4
+
a
6
equals
Q.
If for an
A
.
P
.
a
1
,
a
2
,
a
3
,
.
.
.
.
.
,
a
n
,
.
.
.
.
,
a
1
+
a
3
+
a
5
=
−
12
and
a
1
a
2
a
3
=
8
then the value of
a
2
+
a
4
+
a
6
equals to
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