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Answer:
f(n) = 2n - 3 describes the arithmetic sequence,
-1, 1, 3, 5, 7, 9, 11, 13,.......
Step-by-step explanation:
Function:
A function is like a machine that gives an output for a given input.
A function has an independent variable which is called the input of the function.
The output for a given input is called the dependent variable.
Here. 'n' is the independent variable
f(n) is the function dependent variable i.e function of n as an output.
For Arithmetic sequence
Where
= nth number of the sequence.
a₁ = First term
d = common difference = a₂ - a₁ = a₃ - a₂ = so on
For a function which describes Arithmetic sequence,
a₁ = -1
d = 1 - -1 =2
∴ f(n) = a₁ + (n -1 )d
substituting the values we get
∴ f(n) = -1 +(n-1)2
using distributive property
∴ f(n) = - 1 + 2n - 2
∴ f(n) = 2n - 3 ..........is the required function
and
use the second expression to calculate the left-hand side of the first equation:
Add 10 to both sides if this equation to get
and divide both sides by 2
this proves that x = 17, give the two initial equations