Partial sum of series question (1 Viewer)

[clintmyster]

The sum of the first n terms of a sequence is given by Sn = 3^n - 1. Find the general term, hence the first four terms.

answer is 2{3^(n-1)}

i cant seem to subtract exponentials properly and therefore cannot obtain the general term. Any help would me much appreciated!

 

[clintmyster]

yes that is correct. Oh i didn't know you can show superscript! im guessing that feature comes up when you use 'reply' as opposed to 'quick reply'?

 

[WannaBang?]

No.

Super script {sup}{/sup} (use [] instead of {})
Sub script is the same, but type "sub" instead of "sup"

Now

@ n=1
S₁ = 3¹-1
= 2

So, the first term is 2.

@ n = 2
S₂ = 3²-1
= 8

T₂ = 8 -2
= 6

Keep going until you've done S₄ and found T₄

Then, using the terms (2, 6, 18, 54) you can derive the general term. Takes some "thinking"

But using what you've got

T₁ = 2
T_n = 2(3^n-1)
T₁ = 2(3⁰)
T₁ = 2

Checks. I think it'd be easier to find S(1>4), use this to find the each term, then get your general term.

Is this the way you wanted it, or is there a different ext. way you wanted to see?

Exphate, you're so sexy when you do maths.

 

[clintmyster]

the way i was taught to do it was to find S_n and then S_n-1

the general term is then found by S_n - S_n-1

thats why i was saying i couldnt subtract exponentials. Any help on this method?