Respuesta :
The common difference and the first term of the arithmetic progression are y - 0.5x and 5x - 5y respectively
Arithmetic progression:
The nth term of an arithmetic progression is express as follows:
- nth = a + (n - 1)d
where
n = number of terms
d = common difference
a = first term
The fifth term is represented as t₅ = 3x - y
The 11th term is represented as t₁₁ = 5y
Let's find the first term and the common difference as required.
Therefore,
- a + 4d = 3x - y
- a + 10d = 5y
Take the difference to find d
6d = 5y - 3x + y
6d = 6y - 3x
d = y - 0.5x
Let's find the first term.
a + 4(y - 0.5x) = 3x - y
a + 4y - 2x = 3x - y
a = 3x - y - 4y + 2x
a = 5x - 5y
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