Question

Write the first 6 terms of the sequences whose n terms are given below and classify them as arithmetic progression, geometric progression, arithmetico-geometric progression, harmonic progression and none of them.

(i) 1/2^{n + 1}

(ii) (n + 1)(n + 2)/(n + 3(n + 4))

(iii) 4(1/2)ⁿ

(iv) (-1)ⁿ/n

(v) (2n + 3)/(3n + 4) 

(vi) (3n - 2)/3^{n - 1}

Answer 1

(i) 1/2^{n + 1}

(ii) (n + 1)(n + 2)/(n + 3(n + 4))

So the first six terms are 3/8,3/5,5/6,15/14,21/16,14/9.

It is not a G.P. or A.P. or H.P. or A.G.P.

(iii) 4(1/2)ⁿ

(iv) (-1)ⁿ/n

It is not an A.P. or G.P. or H.P. or A.G.P

(v) (2n + 3)/(3n + 4) 

It is not an A.P. or G.P. or H.P. or A.G.P.

(vi) (3n - 2)/3^{n - 1}

It is a A.G.P.