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

`4 (1/2)^"n"`

Answer 1

Given the n^th term a_n = `4 (1/(2^"n"))`

a₁ = `4 xx 1/2^1` = 2

a₂ = `4 xx 1/2^2 = 4 xx 1/4` = 1

a₃ = `4 xx 1/2^3 = 4 xx 1/8 = 1/2`

a₄ = `4 xx 1/2^4 = 4 xx 1/16 = 1/4`

a₅ = `4 xx 1/2^5 = 4 xx 1/32 = 1/8`

a₆ = `4 xx 1/2^6 = 4 xx 1/64 = 1/16`

∴ The given sequence is 2, 1, `1/2, 1/4, 1/8, 1/16`
First term a₁ = 2
Second term a₂ = 1
r = `"a"_2/"a"_1 = 1/2`

r = `"a"_3/"a"_2 = (1/2)/1 = 1/2`

∴ The given sequence is a G.P with first term a = 2, common ratio r = `1/2`