Geometric progression is a sequence that can be found by multiplying the same value by the preceding number. The next term in the sequence is 8 / 81.
A geometric progression is a sequence of numbers other than 0 and can be estimated by multiplying a specific digit by the prior number. It is given as,
an = a₁rⁿ⁻¹
Where r is the common ratio or the number.
For the given sequence the common ratio (r) is 2/3.
Substituting values:
an = (1/2) × (2/3)ⁿ⁻¹
Applying r:
an=2ⁿ⁻¹ / 2 × 3ⁿ⁻¹
Substitute n to find the nth term as:
a₅=2⁽⁵⁾⁻²/ 3⁽⁵⁾⁻¹
a₅=8/ 3⁽⁵⁾⁻¹
a₅ = 8/ 81
Therefore, the next number on the sequence is 8/81.
Learn more about geometric progression here:
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