SOLUTION: What are the first three terms if the 11th term of an arithmetic sequence is 60 and the sum of the first 11 terms is 55?

Algebra ->  Sequences-and-series -> SOLUTION: What are the first three terms if the 11th term of an arithmetic sequence is 60 and the sum of the first 11 terms is 55?       Log On


   

Question 1118377: What are the first three terms if the 11th term of an
arithmetic sequence is 60 and the sum of the first 11
terms is 55?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
What are the first three terms if the 11th term of an
arithmetic sequence is 60 and the sum of the first 11
terms is 55?

a1,__,__,__,__,__,__,__,__,__,60,...

Sn = (n/2)(a1 + an)

S11 = (11/2)(a1 + a11)

55 = (11/2)(a1 + 60)

Multiply both sides by 2

110 = 11(a1 + 60)

110 = 11a1 + 660

-550 = 11a1

-550/11 = a1

-50 = a1 

So

a1,__,__,__,__,__,__,__,__,__,60,

becomes

-50,__,__,__,__,__,__,__,__,__,60,

To fill in the blanks, we only need the common difference d:

an = a1 + (n - 1)d

 60 = -50 + (11 - 1)d
 60 = -50 + 10d
110 = 10d
 11 = d

So the sequence

-50,__,__,__,__,__,__,__,__,__,60,...

becomes

-50,-39,-28,-17,-6,5,16,27,38,49,60,...

So the first three terms are -50,-39 and -28

Edwin