In an ap first term is 2,the sum of first 5terms is1/4 of the sum of next 5terms .find sum of first 20terms

Asked by sujathahk | 9th Jul, 2019, 08:38: PM

Expert Answer:

 
Here a = 2 
 
According to the condition in the question, we get
 
a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 1/4 [(a + 5d) + (a + 6d) + (a + 7d) + (a + 8d) + (a + 9d)]
 
→ 5a + 10d = 1/4 (5a + 35d)
→ 20a + 40d = 5a + 35d
→ 15a + 5d = 0
→   3a + d = 0
→   d = -3(2) = -6
 

Sn = n/2[2a +(n - 1)d]
→ S20  = 20/2[2 × 2 + (20 - 1)(-6)]
           = 10(4 - 114) 
           = -1100

Answered by Yasmeen Khan | 10th Jul, 2019, 11:32: AM