Question

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

Answer 1

Answer: $n=\dfrac{a_n-a_1}{d}+1$

Step-by-step 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

$\dfrac{a_n-a_1}{d}=n-1$

Now, add 1 to the both sides , we get

$\dfrac{a_n-a_1}{d}+1=n$

Or

$n=\dfrac{a_n-a_1}{d}+1$

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