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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 $S_{20} = \frac{1}{5}$ and $S_{10} = 0,$ then find $S_{70}.$

 Mar 28, 2024
 #1
avatar+128794 
+1

0   +  55d  =   1/5

55d = 1/5

d  =   1 / [ 5 * 55]  =  1 / 275

 

70th term is  0  + 60d  =   60 / 275   =12 / 55

 

S70 =   [  12/55 + 0 ] [70 -10 + 1 ]  / 2   =

 

[12/55] * 61  / 2  =   

 

366 / 55

 

 

cool cool cool

 Mar 28, 2024

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