SOLUTION: What is the S12 for tn= 2(3) ^(n-1) S12 means Sum of 12 I attempted this several times and I got, 1062882, another time I got 531440. I appreciate any help.

Algebra ->  Sequences-and-series -> SOLUTION: What is the S12 for tn= 2(3) ^(n-1) S12 means Sum of 12 I attempted this several times and I got, 1062882, another time I got 531440. I appreciate any help.      Log On


   

Question 1181767: What is the S12 for tn= 2(3) ^(n-1)
S12 means Sum of 12
I attempted this several times and I got, 1062882, another time I got 531440.
I appreciate any help.
Found 4 solutions by math_helper, greenestamps, MathLover1, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
perl -e '$sum=0; for($i=0;$i<12; $i++) { $sum += (2*(3**($i))); print "$sum\n"; }'
2
8
26
80
242
728
2186
6560
19682
59048
177146
531440 <<< sum of first 12 terms

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


S12 = 2(3)^0+2(3)^1+2(3)^2+...+2(3)^(n-1)

S12 = 2((3)^0+(3)^1+(3)^2+...+(3)^(n-1))

Apply the formula for the sum of a finite geometric series:

S12+=+2%28%281-3%5E12%29%2F%281-3%29%29+=+3%5E12-1+=+531440

The second answer you show is correct.

Your first answer is 2%283%5E12%29

It is possible that for that answer you were using the correct formula but did the calculation incorrectly....

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sum%28+2%2A3%5E%28n+-+1%29%2Cn=1%2C12%29=531440

check by finding all terms:

t%5B1%5D=+2%283%29+%5E%281-1%29=2
t%5B2%5D=+2%283%29+%5E%282-1%29=2%2A3%5E1=6
t%5B3%5D=+2%283%29+%5E%283-1%29=2%2A3%5E2=18
t%5B4%5D=+2%283%29+%5E%284-1%29=2%2A3%5E3=54
t%5B5%5D=+2%283%29+%5E%285-1%29=2%2A3%5E4=162
t%5B6%5D=+2%283%29+%5E%286-1%29=2%2A3%5E5=486
t%5B7%5D=+2%283%29+%5E%287-1%29=2%2A3%5E6=1458
t%5B8%5D=+2%283%29+%5E%288-1%29=2%2A3%5E7=4374
t%5B9%5D=+2%283%29+%5E%289-1%29=2%2A3%5E8=13122
t%5B10%5D=+2%283%29+%5E%2810-1%29=2%2A3%5E9=39366
t%5B11%5D=+2%283%29+%5E%2811-1%29=2%2A3%5E10=118098
t%5B12%5D=+2%283%29+%5E%2812-1%29=2%2A3%5E11=354294
sum:
2%2B6%2B18%2B54%2B162%2B486%2B1458%2B4374%2B13122%2B39366%2B118098%2B354294=531440
531440=531440



Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.
On geometric progressions,  see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

You will find there all necessary formulas and explanations,
and will NEVER make that mistakes what you made before . . .

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.