The second, third and sixth terms of an A.P. are consecutive and distinct terms of a G.P. find common ratio
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Answer:
1,3
Step-by-step explanation:
Let the first term of A.P. be a and common difference be d,
Second term = a + d
Third term = a + 2d
Sixth term = a + 5d
Given, that these are the consecutive terms of a G.P.
∴ Common ratio of G.P., r =
a + d
a + 2d
=
a + 2d
a + 5d
Step -2: Find the common ratio.
a + d
a + 2d
=
a + 2d
a + 5d
⇒ (a + 2d)
2
= (a + d)(a + 5d)
⇒ a
2
+ 4ad + 4d
2
= a
2
+ 6ad + 5d
2
⇒ d
2
+ 2ad = 0
⇒ d(d + 2a) = 0
⇒ d = 0 or d = - 2a
When d = 0, the terms of G.P. are a, a, a
∴ The common ratio is 1
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