How many terms (1 Viewer)

[SuxMATH]

3^n - 3^n+1 + 3^n+2 - 3^n+3 +...+ 3^3n

How many terms are there? The answer says 2n+1.

 

[FrankXie]

yes. last-first+1=3n-n+1=2n+1

 

[SuxMATH]

yes. last-first+1=3n-n+1=2n+1

I still don't understand why you just subtracted the highest power and lowest power

 

[Ekman]

I still don't understand why you just subtracted the highest power and lowest power

Well since the powers are increasing incrementally, (by +1), you can find the number of terms by doing last terms power - first terms power+1.
Ill give you a simpler example: How many numbers are there between 1 and 10. 10-1 +1 =10. How about when its between 0 and 10: 10-0+1=11. Since the power indicates how many terms there are(due to the incremental increase), you can calculate the number of terms by doing last power- first power +1.

 

[braintic]

If the sum was 3^1 + 3^2 + 3^3 + ... + 3^9 + 3^10 + 3^11 + ... + 3^20, then there would be 20 terms (powers 1 to 20).
But if the sum was 3^10 + 3^11 + ... + 3^20, the first 9 terms are missing, so there are (20-9) terms.

If the sum was 3^1 + 3^2 + 3^3 + ... + 3^(n-1) + 3^n + 3^(n+1) + ... + 3^3n, there would be 3n terms (powers 1 to 3n).
But if the sum was 3^n + 3^(n+1) + ... + 3^3n, the first (n-1) terms are missing, so there are 3n-(n-1) terms.