SOLUTION: Find the sum of the first 70 terms of the arithmetic sequence: 22,19,16,13 Find the exact sum of the infinite geometric sequence a (1/2), (-1/4),(1/8)

Question 1010826: Find the sum of the first 70 terms of the arithmetic sequence: 22,19,16,13
Find the exact sum of the infinite geometric sequence a (1/2), (-1/4),(1/8)
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Couple of ways to do this...let me show you one way...
Let us find the 70th term, by an = a1 + (n-1)d...
a70 = a1 + 69(-3) = 22 - 207 = -185
Then Sn = (n/2)(a1 + an) = (70/2)(22 - 207) = 35(-185) = -6475
For the second one, it's a bit easier...we use
Sn = a1 / (1 - r) = (1/2) / (1 - (-1/2)) = (1/2) / (3/2) = 1/3
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