Question

Write the first 6 terms of the sequences whose n^th 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)`

Answer 1

a_n = `(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.