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Question
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
Solution
Since (n – 2), (4n – 1) and (5n + 2) are in A.P., we have
(4n – 1) – (n – 2) = (5n + 2) – (4n – 1)
`\implies` 4n – 1 – n + 2 = 5n + 2 – 4n + 1
`\implies` 3n + 1 = n + 3
`\implies` 2n = 2
`\implies` n = 1
∴ (n – 2), (4n – 1) and (5n + 2)
∴ (1 – 2), (4(1) – 1) and (5(1) + 2)
So, the given numbers are –1, 3, 7
`\implies` a = –1 and d = 3 – (–1) = 4
Hence, the next two terms are (7 + 4) and (7 + 2 × 4)
i.e 11 and 15
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