Question

19. The first term in an arithmetic sequence is 5. The fourth term in the sequence is -4. The tenth term is-22. Which fun tion can be used to find the nth term of the arithmetic sequeOfs) = -3 +8

Answer 1

-3n + 8

Step-by-step explanation

The first term of an arithmetic sequence = 5

The fourth term = - 4

The tenth term = -22

The nth term of an arithmetic progression = a(n) + (n - 1) d

Where a = first term

n = number of terms

d = common difference

Firstly, we need to find the common difference

Since, a = 5

T4 = a + (n - 1) d

T4 = 5 + (4 - 1)d\

-4 = 5 + 3d

Collect the like terms

-4 - 5 = 3d

3d = -9

Divide both sides by 3

3d/3 = -9/3

d = -3

The nth term can be calculated using the below function

Tn = a + (n - 1) (-3)

Tn = 5 + -3n + 3

Tn= -3n + 8

The function that can be used to find the nth term of the arithmetic function is f(n) = -3n + 8