Respuesta :

gustanika
The formula of arithmetic sequence is
an = a₁ + d(n - 1)

Then we need to find the formula to determine n. I reverse the equation so the 'n' will be on the left side.
a₁ + d(n - 1) = an

Then I move all the terms on the left one by one to the right side except n
a₁ + d(n - 1) = an
d(n - 1) = an - a₁
n - 1 = (an - a₁)/d
n = 1 + (an - a₁)/d

This is the formula to solve n
n = 1 + (an - a₁)/d
JeanaShupp

Answer: [tex]n=\dfrac{a_n-a_1}{d}+1[/tex]

Step-by-step explanation:

Given : The formula to find a certain number in an arithmetic sequence is

[tex]a_n=a_1+d(n-1)[/tex], where [tex]a_n[/tex] is the nth term , [tex]a_1[/tex] is the first term and d is the common difference.

To solve the formula for n , first subtract [tex]a_1[/tex] from both sides , we get

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

Now, divide d on both sides , we get

[tex]\dfrac{a_n-a_1}{d}=n-1[/tex]

Now, add 1 to the both sides , we get

[tex]\dfrac{a_n-a_1}{d}+1=n[/tex]

Or

[tex]n=\dfrac{a_n-a_1}{d}+1[/tex]

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