SOLUTION: Can you please show me how to work this out? I would really be thankful!! What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms? 1,452 1,728

Algebra ->  Sequences-and-series -> SOLUTION: Can you please show me how to work this out? I would really be thankful!! What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms? 1,452 1,728       Log On


   

Question 881938: Can you please show me how to work this out? I would really be thankful!!
What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms?
1,452
1,728
2,028
2,268
Found 2 solutions by ewatrrr, jim_thompson5910:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
{3, 9, 15, ...}
Arithmetic Sequence: d = 6
Note typo here
a[26] = 3 + 25d = 3 + ++highlight_green%28150%29+
S%5Bn%5D=%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2
S[26] = 26(3 + 153)/2 = 2,208

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The common difference is 9 - 3 = 6. So d = 6

First term: a1 = 3


Sn = n*(a1 + an)/2


Sn = n*(a1 + a1 + (n-1)*d)/2


Sn = n*(2*a1 + (n-1)*d)/2


S26 = 26*(2*a1 + (26-1)*d)/2 ... plug in n = 26


S26 = 26*(2*3 + (26-1)*d)/2 ... plug in a1 = 3


S26 = 26*(2*3 + (26-1)*6)/2 ... plug in d = 6


S26 = 2,028


The sum of the first 26 terms is 2,028