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Question
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
`1/(2^("n"+ 1))`
Solution
an = `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`
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