Respuesta :

kudzordzifrancis
ANSWER

[tex] \boxed {f(n) = 7n - 4}[/tex]


EXPLANATION


From the table,

[tex]a_1 = 3[/tex]


[tex]a_2 = 10[/tex]




There is a constant difference of

[tex]d = a_2 - a_1[/tex]


[tex]d = 10 - 3 = 7[/tex]


The sequence is therefore an arithmetic progression.

The general formula for the arithmetic progression is

[tex]f(n) = a_1 + (n - 1)d[/tex]

We substitute the values into the formula to obtain,

[tex]f(n) = 3+ 7(n - 1)[/tex]



We expand the bracket to obtain,

[tex]f(n) = 3+ 7n - 7[/tex]


This simplifies to

[tex]f(n) =7n - 4[/tex]


zainebamir540

Answer:

Choice B is correct answer.

Step-by-step explanation:

From given data,we observe that

a₁ = 3 and a₂ = 10 and a₃ = 17

Then the difference d  between the successive terms is 7.

d = 7 which is constant.

Therefore, it is arithematic progression.

The formula for nth term of arithematic progression is :

f(n)  = aₙ = a₁ + (n-1)d

putting above values in formula,we get

f(n) = 3+ (n-1)7

f(n) = 3+7n-7

f(n) = 7n-4 which is the answer.





































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