If a, start subscript, 1, end subscript, equals, 4a 1 =4 and a, start subscript, n, end subscript, equals, a, start subscript, n, minus, 1, end subscript, plus, 1a n =a n−1 +1 then find the value of a, start subscript, 5, end subscripta 5
Question
If a, start subscript, 1, end subscript, equals, 4a 1 =4 and a, start subscript, n, end subscript, equals, a, start subscript, n, minus, 1, end subscript, plus, 1a n =a n−1 +1 then find the value of a, start subscript, 5, end subscripta 5
Solution
The given sequence is a recursive sequence where each term is defined as the previous term plus 1.
Given that a₁ = 4, we can find the subsequent terms as follows:
a₂ = a₁ + 1 = 4 + 1 = 5 a₃ = a₂ + 1 = 5 + 1 = 6 a₄ = a₃ + 1 = 6 + 1 = 7 a₅ = a₄ + 1 = 7 + 1 = 8
So, the value of a₅ is 8.
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