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fiasKO [112]
3 years ago
14

What is the difference between the reciprocal and the opposite of a fraction? Plz help!

Mathematics
1 answer:
aliina [53]3 years ago
4 0
A reciprocal is when you flip the numerator and denominator.

Opposite just means multiplying the fraction by -1.
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Pikachu is right.

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Select the common ratio and the 4th term of the geometric series: 9, -6,4...
Blababa [14]

The given geometric sequence has the common ratio, <u>r = -2/3</u>, and the value of the 4th term, <u>a₄ = -8/3</u>.

A geometric sequence is a special series where every term is the product of the previous term and a common ratio.

The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.

In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........

The first term of the sequence, a = 9.

The second term of the sequence, a₂ = -6.

By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:

a₂ = a.r²⁻¹.

Substituting the values, we get:

-6 = 9(r²⁻¹),

or, r²⁻¹ = -6/9,

or, r = -2/3.

Thus, the common ratio of the given geometric sequence is <u>-2/3</u>.

The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:

a₄ = a.r⁴⁻¹ = a.r³.

Substituting the values, we get:

a₄ = 9(-2/3)³,

or, a₄ = 9.(-8/27),

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