Find an equation for the nth term of the arithmetic sequence.a16 = 21, a17 = -1

Question

Find an equation for the nth term of the arithmetic sequence.a16 = 21, a17 = -1

an = 351 + 22(n + 1)
an = 351 - 22(n + 1)
an = 351 + 22(n - 1)
an = 351 - 22(n - 1)

Answer 1

Since the sequence is arithmetic, we can find any term of the sequence by adding the same number (the common difference, d) to the preceding term.  

 

So, a₁₇ = a₁₆ + d

 

        -1 = 21 + d

 

         d = -22

 

The nth term, a_n, of an arithmetic sequence can be found by the formula a_n = a₁ + (n-1)d

 

               a₁₇ = a₁ + 16d

 

                  -1 = a₁ + 16(-22)

 

                a₁ = -1 + 16(22) = 351

 

Therefore, a_n = 351 - 22(n-1)