The first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.
What is a geometric progression?
When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied with that constant term to form a geometric progression.
The recursive formula allows us to find a term in a sequence from the previous term.
Given
[tex]a_n=\dfrac{a_n-1}{4}[/tex]
Given the fourth term, we require to work back to the third term, second, and so on. Rearrange the formula to give.
Multiply both sides by 4, then
a[tex]_{n-1}[/tex] = 4a[tex]._n[/tex]
Given a₄ = 2, then
The first four terms will be calculated as given below:-
a₃ = 4 × a₄ = 4 × 2 = 9
a₂ = 4 × a₃ = 4 × 9 = 36
a₁ = 4 × a₂ = 4 × 36 = 144
Therefore, the first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.
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