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Byju's Answer
Standard XII
Mathematics
Harmonic Progression
the second te...
Question
the second term of an A.P is (x-y) and the fifth term is (x+y) find the first term of the AP
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Solution
Let
a
be
the
first
term
and
d
be
the
common
difference
.
Now
,
a
2
=
x
-
y
⇒
a
+
d
=
x
-
y
.
.
.
.
.
1
Now
,
a
5
=
x
+
y
⇒
a
+
4
d
=
x
+
y
.
.
.
.
.
2
Subtracting
1
from
2
,
we
get
4
d
-
d
=
x
+
y
-
x
-
y
⇒
3
d
=
x
+
y
-
x
+
y
⇒
3
d
=
2
y
⇒
d
=
2
y
3
Now
,
from
1
,
we
get
a
+
2
y
3
=
x
-
y
⇒
a
=
x
-
y
-
2
y
3
⇒
a
=
3
x
-
3
y
-
2
y
3
⇒
a
=
3
x
-
5
y
3
So
,
first
term
,
a
=
3
x
-
5
y
3
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