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If a, start subscript, 1, end subscript, equals, 9a 1​ =9 and a, start subscript, n, end subscript, equals, a, start subscript, n, minus, 1, end subscript, minus, 5a n​ =a n−1​ −5 then find the value of a, start subscript, 6, end subscripta 6​ .

Question

If a, start subscript, 1, end subscript, equals, 9a 1​ =9 and a, start subscript, n, end subscript, equals, a, start subscript, n, minus, 1, end subscript, minus, 5a n​ =a n−1​ −5 then find the value of a, start subscript, 6, end subscripta 6​ .

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Solution

The problem is a recursive sequence where each term is defined based on the previous term.

Given: a₁ = 9 aₙ = aₙ₋₁ - 5

We need to find the value of a₆.

We can start by finding the values of a₂, a₃, a₄, a₅, and a₆ using the given recursive formula.

a₂ = a₁ - 5 = 9 - 5 = 4 a₃ = a₂ - 5 = 4 - 5 = -1 a₄ = a₃ - 5 = -1 - 5 = -6 a₅ = a₄ - 5 = -6 - 5 = -11 a₆ = a₅ - 5 = -11 - 5 = -16

So, the value of a₆ is -16.

This problem has been solved

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