Question

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

Answer 1

Answer:

-1078

Step-by-step explanation:

n=0 is the first term in the sequence.

Every next term is 20 less then the previous term.

In Mathematics you can write this as follows:

f(n) = f(0) - (n-1)*20

f(n) = f(0) - {(n-1)*20}

f(n) = f(0) - {(20n) -20}

Attention: Please note that -1 * -20 = +20

f(n) = f(0) - 20n + 20

Check yourself, find f(2):

f(0) = 2

f(2) = 2 - 20*2 + 20

f(2) = 2 - 40 + 20

f(2) = 2 - 20

f(2) = -18

Check yourself once more, find f(3):

f(0) = 2

f(3) = 2 - 20*3 + 20

f(3) = 2 - 60 + 20

f(3) = 2 - 40

f(3) = -38

Now just find f(55):

f(55) = 2

f(55) = 2 - 20*55 + 20

f(55) = 2 - 1100 + 20

f(55) = 2 - 1080

f(55) = -1078