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if x 32 z are in ap x 3 z are in gp then which one
Question:
If
x
,
3
2
,
z
are in
A
P
;
x
,
3
,
z
are in GP; then which one of the following will be in HP?
WBJEE
Updated On:
Apr 23, 2024
(A)
x
,
6
,
z
(B)
x
,
4
,
z
(C)
x
,
2
,
z
(D)
x
,
1
,
z
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Verified By Collegedunia
The Correct Option is
A
Solution and Explanation
Explanation:
Given:
x
,
3
2
,
z
are in
A
P
∴
2
×
3
2
=
x
+
z
⇒
x
+
z
=
3
…
.1
Now,
x
,
3
,
z
are in GP
∴
3
2
=
x
z
⇒
x
z
=
9
…
.2
Let
x
,
y
,
z
are in
H
P
∴
y
=
2
x
z
x
+
z
=
2
×
9
3
=
6
So,
x
,
6
,
z
are in HP.Hence, the correct option is (A).
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