the formula for the nth term of an arithmetic sequence can be found using the formula (a_{n}=a_{1}+(n…

the formula for the nth term of an arithmetic sequence can be found using the formula (a_{n}=a_{1}+(n - 1)d). which of the following is equivalent to this equation?\n(n=a_{n}+a_{1})\n(n=\frac{a_{n}+a_{1}-d}{d})\n(n=a_{n}-a_{1})\n(n=\frac{a_{n}-a_{1}+d}{d})

the formula for the nth term of an arithmetic sequence can be found using the formula (a_{n}=a_{1}+(n - 1)d). which of the following is equivalent to this equation?\n(n=a_{n}+a_{1})\n(n=\frac{a_{n}+a_{1}-d}{d})\n(n=a_{n}-a_{1})\n(n=\frac{a_{n}-a_{1}+d}{d})

Answer

Explanation:

Step1: Start with the formula

$a_n=a_1+(n - 1)d$

Step2: Expand the right - hand side

$a_n=a_1+nd - d$

Step3: Isolate the terms with $n$

$a_n - a_1 + d=nd$

Step4: Solve for $n$

$n=\frac{a_n - a_1 + d}{d}$

Answer:

$n=\frac{a_n - a_1 + d}{d}$ (the fourth option)