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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 $S_1 = \frac{1}{5}$ and $S_2 = \frac{1}{10},$ then find $S_{15}.$

 Jun 8, 2024
 #1
avatar+129399 
+1

S1 = a1 = 1/5

S2  = 2a1 + d

1/10 = 2/5 +  d

1/10 - 2/5 = d

d  =  -3/10

 

 

sum of the first n terms of an  arithmetic sequence  =

 

(n)*a1 +  (n)(n-1)/2 *d

 

S15  =  (15 ) (1/5)  + (15)(14)/2 * (-3/10)  =   3 - 63/2  = -57/2  = - 28.5

 

cool cool cool

 Jun 8, 2024
edited by CPhill  Jun 8, 2024

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