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NDA Math Sequences and Series
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© examsnet.com
Question : 25
Total: 79
If 3rd, 8th and 13th terms of a GP are p, q and r respectively, then which one of the following is correct?
[NDA II 2019]
q
2
=
p
r
r
2
=
p
q
pqr = 1
2
q
=
p
+
r
Validate
Solution:
Let a be the first term and k be the common ratio of a G.P.
Then, 3rd term
=
t
3
=
a
k
3
–
1
=
p
⇒
a
k
2
=
p
....(i)
8th term
=
t
8
=
a
k
8
–
1
=
q
a
k
7
=
q
...(ii)
and, 13th term
=
t
13
=
a
k
13
–
1
=
r
⇒
a
k
12
=
r
....(iii)
From (ii), divided by (i), we get
a
k
7
a
k
2
=
q
p
⇒
k
5
=
q
p
...(iv)
From (iii), divided by (ii), we get
a
k
12
a
k
7
=
r
q
⇒
k
5
=
r
q
....(v)
From (i) and (ii), we get
q
p
=
r
p
⇒
q
2
=
p
q
r
© examsnet.com
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