Find the indicated term for each sequence.

Question

anonymous · Answer

a. 6, 4, 2, 0, ...a21

b. 3, -6, 12, -24, ...a18

c. 1/3, -2/9, 4/27, -8/81, ...a9

d. 5, -2, -9, -16, ...a120

mathslover · Answer

I will solve any one for you, which one you want?

anonymous · Answer

Can you do B?

mathslover · Answer

well can you first tell me whether it is GP or AP?

anonymous · Answer

I think it's AP

mathslover · Answer

What is the main condition for AP @LoveToDance22 ?

anonymous · Answer

It's if the sequence is adding or subtracting, right?

mathslover · Answer

Well, actually the main thing is the "common difference" like : 1,2,3,4,5 .... , in this sequence the common difference exists which is : 1.

We have the following sequence : 

3 , -6 , 12 , -24 , .... 

Now, can you tell me whether the common difference exists or not?

mathslover · Answer

@LoveToDance22 , you there?

anonymous · Answer

Sorry, stepped away for a second, Is it -2?

mathslover · Answer

No, well, -2 is the common ratio here. 

See this : 

3 * -2 = -6 * -2 = 12 * -2 = -24 * -2 = 48 .... and so on

mathslover · Answer

That is it is a GP...

mathslover · Answer

getting it?

anonymous · Answer

Yeah, thanks! I can do the rest later though, g2g to school :q

mathslover · Answer

You have to just use the following formula : 

$a_n = a * r^{n-1} $

mathslover · Answer

where n = 18 , and r =common ratio =  -2 and a = first term = 3