Sequence & Series question (1 Viewer)

[tempco]

the sum of the first 5 terms of a geometric series is 77 and the sum of the next 5 terms is -2464. find the 4th term of the sequence

Erm.. got that from a friend.. tried a few things, but it didn't work out... help anyone?

Thanks.

 

[coroneos]

That question is impossible. Are you sure that question is correct?
I am the expert at sequences and series. That is not doable!

 

[tempco]

Worked it out.. don't worry about it.

Anyone want to know how it's done?

 

[coroneos]

yeah.. i worked it out as well - easiest question in da world

 

[tempco]

Meh... stuff suspense...

Get the equation of the sum of T1-T5, and T1-T10 - T6-T10

Divide the two equations, along with it's values (77 and -2464) and you should get r = -2, and T4 = -88.

EDIT: I think I did a few silly mistakes with the T4... correct me if I'm wrong.

Originally posted by coroneos
yeah.. i worked it out as well - easiest question in da world

Hehe... that's nice to hear

 

[coroneos]

Okay here is another question:

The Sequence Tn = 2 x 3^n + 3 x 2^n is the sum of two GPs. Find Sn.

 

[tempco]

Is the answer 3(3^n-1) + 6(2^n-1)?

 

[TimTheTutor]

I agree with the above answer given. Just apply the sum of a GP formula separately 2 each of the two GP's then add sums 2gether.
ie. G1: a = 2*3^1 = 6 , r = 3
G2: a = 3*2^1 = 6, r = 2