Since, the first three term of a sequence are 10, 5, 5/2 and the next 6th term 0.3125.This is a geometric sequence since there is a common ratio between each term.
In this case, multiplying the previous term in the sequence by 3 gives the next term.
In other words, aₙ=a₁r⁽ⁿ⁻¹⁾.
Geometric Sequence: r = 1/2
This is the form of a geometry: aₙ=a₁r⁽ⁿ⁻¹⁾According to the question,
This is a geometric sequence with common ratio :
5/10 = 1/2 and, 5/2 ÷ 2 = 1/2
So the 6th term = a r⁽ⁿ⁻¹⁾
= 10 × (1/2)⁵
= 10 × 0.03125
= 0.3125 Therefore, the 6th term is 0.3125.
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