Question

The first term of an arithmetic sequence is 5 and the ninth term is - 19.

a. Find the common difference
b. Write the recursive rule of the arithmetic sequence.

Answer 1

Explanation:

a=5

T9=-19

(a)

`t9 = a + 8d \\ - 19 = 5 + 8d \\ - 19 - 5 = 8d \\ - 24 = 8d \\ (8d)/(8) = ( - 24)/(8) \\ d = - 3`

(b)

Tn=a+(n-1)d

Tn= 5+(n-1)-3

Tn=-3n+3+5

Tn= -3n+8