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प्रश्न
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
`4 (1/2)^"n"`
उत्तर
Given the nth term an = `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`
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