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Byju's Answer
Standard X
Mathematics
Nth Term of a GP
Three numbers...
Question
Three numbers form a GP .if the third term is decreased by 128 then the three number,thus obtained ,will form an AP .if the second term of this AP is decreased by 16 a GP will be formed again.Determine the numbers
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Solution
Dear student
Let
the
three
numbers
in
GP
be
a
r
,
a
,
ar
If
third
term
is
decreased
by
128
then
it
will
become
ar
-
128
So
,
a
r
,
a
,
ar
-
128
is
in
A
.
P
2
a
=
a
r
+
ar
-
128
2
ar
=
a
+
ar
2
-
128
r
.
.
.
.
(
1
)
Now
,
second
term
is
decreased
by
16
i
.
e
.
,
a
-
16
So
,
a
r
,
a
-
16
,
ar
-
128
is
in
G
.
P
a
-
16
2
=
a
r
ar
-
128
a
2
+
256
-
32
a
=
a
2
-
128
a
r
256
-
32
a
=
-
128
a
r
16
-
2
a
=
-
8
a
r
16
r
-
2
ar
+
8
a
=
-
0
8
r
-
ar
+
4
a
=
0
r
8
-
a
+
4
a
=
0
r
=
4
a
8
-
a
.
.
.
.
.
(
2
)
Put
the
value
of
r
in
eq
(
1
)
,
we
get
2
ar
=
a
+
ar
2
-
128
r
2
a
4
a
8
-
a
=
a
+
a
4
a
8
-
a
2
-
128
4
a
8
-
a
8
a
2
8
-
a
=
a
8
-
a
2
+
16
a
3
-
512
a
8
-
a
64
a
2
-
8
a
3
=
64
a
+
a
3
-
16
a
2
+
16
a
3
-
4096
a
+
512
a
2
25
a
3
+
432
a
2
-
4032
a
=
0
(
a
+
24
)
(
25
a
-
168
)
=
0
a
=
-
24
or
a
=
168
25
so
,
when
a
=
-
24
then
r
=
4
-
24
8
+
24
=
-
3
When
a
=
168
25
then
r
=
4
168
25
8
-
168
25
=
21
So
,
number
are
8
,
-
24
,
72
or
8
25
,
168
25
,
3528
25
Regarfds
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