Expert: Sherman D. - 7/9/2009

Question
  Sn =  (a1 + an)    or    Sn =  [2a1 + (n – 1)d]     
1. Find the sum of the first twelve terms of  15, 22, 29,…..
2.Find the sum of the first 50 positive multiples of 5.

3..Find the sum of the integers from 19 to 81, inclusive.

4. Find the sum of the first 100 positive even integers.  

Answer
1.)
a(n) = 15 + 7(n - 1)

a(12) = 15 + 7(12 - 1) =

S(12) = (12/2)(15 + 92) = 642

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2.)
5, 10, 15, 20, ...

a(n) = 5 + 5(n - 1)

a(50) = 5 + 5(50 - 1) = 250

S(50) = (50/2)(5 + 250) = 6375

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3.)
a(n) = 19 + (n - 1)
81 = 19 + (n - 1)
62 = n - 1
n = 63

S(63) = (63/2)(19 + 81) = 3150

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4.)
2, 4, 6, 8, ....

a(n) = 2 + 2(n - 1)

a(100) = 2 + 2(100 - 1) = 200

S(100) = (100/2)(2 + 200) = 5050

info found at
www.ltcconline.net/greenl/Courses/103B/seqSeries/ARITSEQ.HTM

Not certain where you got Sn = a1 + an or Sn = 2a1 + (n - 1)d