What is the simple formula for the nth term of the following arithmetic sequence? 6, 2, -2, -6, -10..

Question

Cant seem to solve this one, can anybody get the answer for me?

Answer 1

nth term =    a+(n-1)d

a=6

d=-4

nth term = 6+(n-1)-4

              =6-4n+4

              =10-4n   

Answer 2

each term is 4 less than the previous term.

therefore the difference d = -4

Each term starting from the beginning can be found by repeatedly subtracting 4 from the first term.

 

For the second term, subtract 4 from 6

For the third term, subtract 4 twice from 6

For the fourth term, subtract 3 4's from 6

 

So we see a pattern that the number of 4's subtracted is one less than the position of the term

 

If a₁ is the first term and a_n is the nth term, then

 

a_{n =} a₁ + (n-1)d        a₁ =6 and d = -4

 

a_n = 6 - 4(n-1)

 

a_n = 10 - 4n