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Question
Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them
`(2"n" + 3)/(3"n" + 4)`
Solution
an = `(2"n" + 3)/(3"n" + 4)`
a1 = `(2 xx 1 + 3)/(3 xx 1 + 4) = (2 + 3)/(3 + 4) = 5/7`
a2 = `(2 xx 2 + 3)/(3 xx 2 + 4) = (4 + 3)/(6 + 4) = 7/10`
a3 = `(2 xx 3 + 3)/(3 xx 3 + 4) = (6 + 3)/(9 + 4) = 9/13`
a4 = `(2 xx 4 + 3)/(3 xx 4 + 4) = (8 + 3)/(12 + 4) = 11/16`
a5 = `(2 xx 5 + 3)/(3 xx 5 + 4) = (10 + 3)/(15 + 4) = 13/19`
a6 = `(2 xx 6 + 3)/(3 xx 6 + 4) = (12 + 3)/(18 + 4) = 15/22`
∴ The given dequence is `5/7, 7/10, 9/13, 11/6, 13/19, 15/22`, .........
This is neither A.P, G.P nor AGP.
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