Question

What is the missing value in the table below?

Answer 1

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The missing value in the table below is 343. The correct option is A.

What is geometrical series?

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

The given table if closely observed forms a geometric progression, this is because the value of the dependent variable, y is increasing by a common ratio. The common ratio in the table is,

Common ratio = y₂/y₁ = 1/(1/7) = 7

Now, for any geometric progression, the value of the nth term is given as,

Tₙ = a₁ (r)⁽ⁿ⁻¹⁾

where a₁ is the first term of the geometric progression and r is the common ratio. Therefore, the nth term of the series is,

T = a₁ (r)⁽ⁿ⁻¹⁾

Tₙ = (1/7) (7)⁽ⁿ⁻¹⁾

y = (1/7)(7)⁽ˣ⁻¹⁾

Now, the value of the y when the value of x is 5 is,

y = (1/7)(7)⁽ˣ⁻¹⁾

y = (1/7)(7)⁽⁵⁻¹⁾

y = (1/7)(7)⁴

y = (1/7) × 2401

y = 343

Hence, the missing value in the table below is 343.

Learn more about Geometrical Series here:

brainly.com/question/4617980

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