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Let a_1, a_2, a_3, \dots be an arithmetic sequence.  Let $S_n$ denote the sum of the first $n$ terms.  If $S_1 = \frac{1}{2}$ and $S_{2} = \frac{1}{2},$ then find $S_{15}.$

 Apr 9, 2024

Best Answer 

 #1
avatar+214 
+1

If \(S_1\) is 1/2

that means \(a_1\) is 1/2.

If \(a_1 \) is 1/2, then \(a_2\) is 0

So \(a_{15}\) is 1/2 - 14(1/2) = 13/2

So 1/2 + 13/2 = 7

7 times 15/2 = 105/2

smileycoolsmiley

 Apr 10, 2024
 #1
avatar+214 
+1
Best Answer

If \(S_1\) is 1/2

that means \(a_1\) is 1/2.

If \(a_1 \) is 1/2, then \(a_2\) is 0

So \(a_{15}\) is 1/2 - 14(1/2) = 13/2

So 1/2 + 13/2 = 7

7 times 15/2 = 105/2

smileycoolsmiley

aboslutelydestroying Apr 10, 2024

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