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

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

Answer 1

a_n = `1/(2^("n" + 1))`

a₁ = `1/(2^(1 + 1)) = 1/2^2`

a₂ = `1/(2^(2 + 1)) = 1/2^3`

a₃ = `1/(2^(3 + 1)) = 1/2^4`

a₄ = `1/(2^(4 + 1)) = 1/2^5`

a₅ = `1/(2^(5 + 1)) = 1/2^6`

a₆ = `1/(2^(6 + 1)) = 1/2^7`

Thus the sequence is `1/2^2, 1/2^3, 1/2^4, 1/2^5, 1/2^6, 1/2^7`

r = `"a"_2/"a"_1`

= `(1/2^3)/(1/2^2)`

= `1/2^3 xx 2^2/1`

= `1/2`

∴ The given sequqnce is a Geometric progression, with first term a = `1/2^2` and comon ratio r = `1/2`