Question

The formula to find a certain number in an arithmetic sequence is an=a1+d(n−1)an=a1+d(n−1) .

Solve for n

Answer 1

Answer:
`n=(a_n-a_1)/(d)+1`

Explanation:

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

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

To solve the formula for n , first subtract
`a_1` from both sides , we get

`a_n-a_1=d(n-1)`

Now, divide d on both sides , we get

`(a_n-a_1)/(d)=n-1`

Now, add 1 to the both sides , we get

`(a_n-a_1)/(d)+1=n`

Or

`n=(a_n-a_1)/(d)+1`

Answer 2

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