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NDA Math Sequences and Series
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© examsnet.com
Question : 34
Total: 79
The numbers 1, 5 and 25 can be three terms (not necessarily consecutive) of
[NDA I 2019]
only one AP
more than one but finite number of AP's
infinite number of AP's
finite number of GP's
Validate
Solution:
(C)
Let for AP,
t
1
= 1,
t
p
= 5,
t
q
= 25, c .d = d
∴ 1+( p−1 )d = 5 ⇒ ( p−1) d = 4 …(i)
1 + (q−1) d = 25 ⇒ (q−1) d = 24 …(ii)
∴ from (i) and (ii)
q
−
1
p
−
1
= 6 ⇒ q−1 = 6 p − 6
⇒ 6 p − q = 5
∴ there are infinite AP possible.
In same ways, we can show that infinite GP are possible.
© examsnet.com
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