Question

PLEASE HELP AND SHOW ALL WORK:
List the first four terms of a geometric sequence with T1 = 4 and Tn = -3Tn-1.

Answer 1

t1= 4 \[Tn = (-3)^{n-1}\]

Like that ?

Answer 2

no like Tn= -3t^(n-1)

Answer 3

wait i got it wrong like this

Answer 4

well its saying to get the next term multiply the previous turn by -3

so if the 1st term is 4

then 2nd term is T2 = -3 x 4 a negative value

3rd term T3 = -3 x T3 a positive value

4th term T4 = -4 x T3 a negative value

Answer 5

oops T3 = -3 x T2

Answer 6

and T4 = -3 x T3

Answer 7

sorry for the typos

Answer 8

But i'm confused over what Tn=-3Tn-1 means like how to substitute it or something
and its fine

Answer 9

ok... what they needed to say is that n >= 2

so you know \[T_{1} = 4\]


now let n = 2 using the formula

\[T_{2} = -3 \times T_{2 -1}...so.... T_{2} = -3 \times T_{1}\]

and when n = 3

\[T_{3} = -3 \times T_{3 -1}\]

which is \[T_{3} = -3 \times T_{2}\]


so all the subscript is doing is telling you the position of the term in the sequence

Answer 10

oh that makes more sense so you're basically just multiplying by -3 to find each term?

Answer 11

thats correct...

Answer 12

ok thank you so much

Answer 13

glad to help