Question

Find the first six terms of the sequence.

a1 = -8, an = 5 • an-1

Answer 1

This sequence is recursive. Meaning it requires an intial term to be given for one to solve for the next terms of the sequence. We are given a1, and an = 5 * an-1. This just means that the next term is equal to the previous term times 5. So we can use the already given a1, to solve for a2 like this:\[a _{n}= 5 \times a _{n-1} \implies a _{2}=5 \times a _{2-1}=5 \times a_{1}=5 \times (-8)=-40\]So now we know a2, we can repeat the same procedure to find the next however many terms we need to. Can you do the same and find the next 5 more terms?

@Ambition

Answer 2

@Genius12 do I do 5x (-40) to get the next term?

Answer 3

Exactly. To find a3, we do 5 x a2, and since a2 = -40, we plug that in and we get 5 x (-40). So that's right and keep doing that until you got all the terms you need to find.

@Ambition

Answer 4

@genius12 so a1 = -8
a2 = -40
a3 = -200
a4 = -1000
a5= -5000
a6 = -25,000