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Question
Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.
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Solution
Let the five numbers in G.P. be `"a"/"r"^2, "a"/"r", "a", "ar","ar"^2`
According to the given conditions,
`"a"/"r"^2 xx "a"/"r" xx "a" xx "ar" xx "ar"^2` = 1024
∴ a5 = 45
∴ a = 4 ...(i)
Also, ar2 = a2
∴ r2 = a
∴ r2 = 4 ...[From (i)]
∴ r = ± 2
When a = 4, r = 2
`"a"/"r"^2` = 1, `"a"/"r"` = 2, a = 4, ar = 8, ar2 = 16
When a = 4, r = – 2
`"a"/"r"^2` = 1, `"a"/"r"` = −2, a = 4, ar = −8, ar2 = 16
∴ the five numbers are 1, 2, 4, 8, 16 or 1, – 2, 4, – 8, 16.
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