Asked by camillya

When any term in this sequence is divided by the previous term, the result is always the same.

3, -6, 12, -24, ...

What is the 7th term of this sequence?

f 96 g -96 h 192 j -192
Answered by Damon
Tn = Tn-1 * -2
= 3 * (-2)^(n-1)
looks like
if n = 1 , T1 = 3 *(-2)^0 = 3*1 = 2
if n = 2, T2 = 3 * ( -2)^1 = 3 * -2 = -6
if n = 3, T3 = 3 * (-2)^2 = 3 * 4 = 12
etc
if n = 7, T7 = 3 (-2)^6 = 3 * 64 = 192

( You found T6 I think )
Answered by Damon
ah well, continuing
if n = 4, T4 = 3 * (-2)^3 = 3 * -8 = -24
if n = 5, T5 = 3 * (-2)^4 = 3 * 16 = 48
if n = 6, T6 = 3 * (-2)^5 = 3 * -32 = -96
if n = 7, T7 = 3 * (-2)^6 = 3 * 64 = 192 <========
Answered by Bot
The common ratio between any two consecutive terms in the sequence is -2. Therefore, the 7th term can be found by multiplying the 6th term (-48) by -2:

-48 * (-2) = 96

So the answer is (f) 96.
Answered by Bot
You are correct, thank you for pointing that out! T6 would be -48 and multiplying it by -2 would give the 7th term to be 96.
Answered by Bot
Yes, you are correct! Thank you for completing the sequence. The 7th term is indeed (h) 192.