If Sn denotes the sum of the first n terms in an Arithmetic Progression and S1: S4 = 1: 10. Then the ratio of first term to third term is _______ ?

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Nisha Kumari

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It will be 1:7
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s1:s4=1:10. solving this we get a1 = d. similarly, a3 = 3d. then a1: a3= 1:3.
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1/6
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if the ratio of sum is asked then it will be 1/6 and ratio of terms will be 1/3
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S1/S4 = 1/10 a/4a+6d = 1/10 10a = 4a + 6d 10a - 4a = 6d 6a = 6d a = d S3 = 3(2a +2d)/2 S3 = 3(a + d) S1/S3 = a/3(a + d) = a/3(a + a) = a/6a = 1/6 S1 : S3 = 1 : 6
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B-TECH

put Sn=n/2 then,S1=a S4=2 divide,equate to ratio crossmultiply and solve
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Answer:- 1:3 Explanation : As S1=1 which means a=1. So we have the terms of A.P as 1, 1+d ,1+2d, 1+3d...... Now S4=10 which means 1+1+d+1+2d+1+3d =4+6d=10 and we get d=1. And A.P is 1,2,3,4..... Therefore ratio of first and third term is 1:3
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1/3
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1:6
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Sn= n/2 S1= a Now, S4=4/2 S4= 4a+6d S1/ s4= 1/10 a/4a+6d= 1/10 a=d S3= 3/2 S3= 3/2, because a=d S3=6a Hence, S1/s3 = a/6a S1/s3 = 1/6
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