Question

Find the 75th term of the arithmetic sequence -17, -13, -9, ... ​

Answer 1

-17 + 4=-13 and -13+4= -9 so you can set up the equation -17+4x in your calc and hit 2nd graph, window, and enter in 76 and the answer is 287

Answer 2

Explanation:

An arithmetic sequence is one in which the rate at which the terms increase or decrease is linear. Each term differ by a common difference, d. The common difference is determined by subtracting a term from the term that it is following consecutively. It is constant for all consecutive terms. The formula for the nth term of an arithmetic sequence is

Tn = a + (n - 1)d

Where

Tn is the nth term

a is the first term

d is the common difference

n is the number terms.

From the given sequence,

a = - 17

d = - 13 - - 17 = - 9 - - 13

d = 4

n = 75

To find the 75th term, T75, it becomes

T75 = - 17 + (75 - 1)3

T75 = - 17 + 222

T75 = 205