Question

Find the 55th term of the arithmetic sequence 2, -18, -38, ...2,−18,−38,...

Answer 1

Answer:

-1078

Step-by-step explanation:

Notice that each new term of 2, -18, -38 is found by subtracting 20 from the previous term.

Note that a(2) = first term - 20, or

                a(2) =        2       -20(2-1), or

                a(3) =        2       -20(3-1)   =    2 -20(2) = 2 - 40 = -38 (this is right)

So the nth term is a(n) = 2 - 20(n-1)

and the 55th term is a(55) = 2 - 20(55-1) = 2 - 20(54) = -1078

The 55th term is -1078.

Answer 2

You need to use this equation:

an=a1+ d(n−1 )