Question

Write a recursive formula for each sequence. 80, -40, 20.-10. ... O a. a = 80, a, = -40an-1, n 2 Ob. a = 80, an = 400,-1, n22 Oc. a, = 80, a, = -0.51,-1, n 2 2 O d. a, = 80, a, = 0.5an. 1, n 22

Answer 1

$\text{Answer : a}_{n\text{ }}=-0.5a_{n\text{ - 1}}_{}_{}_{}_{}_{}$

Given the sequence

80, -40, 20, - 10

Firstly, we need to find the common ratio

Common ratio

-40/80 = -1/2

20/-40 = -1/2

-10/20 = -1/2

Therefore, the common ratio for this sequence is -1/2

The first term of this sequence = 80

The above the sequence is a geometric sequence

Where a = 80 and r = -0.5

$\begin{gathered} a_n=a_{n\text{ - 1 }}\text{ x r} \\ r\text{ = - 0.5} \\ a_{n\text{ }}=a_{n\text{ - 1}}\text{ x (-0.5)} \\ a_n=-0.5a_{n-1} \end{gathered}$