Question

the sum of first n terms of 3 ap are s1 s2 s3.the first term of each is unity and their common difference are 1,2 and 3 respectively .prove that S1 +S3=2S2

Answer 1

s1 +s3 = 2s2. a + a+ 2d =2* a+d. 2a+2d =2.a+d 2a+2d = 2a+2d Hence proved

Answer 2

Answer:

Step-by-step explanation:

let a be the first term and d the common difference

A.T.Q.

S1 = n/2 [2a + (n-1)d1]

=n/2 [2 + (n-1)] (putting a as 1 and d as 1)

= n/2 [n+1]

S2= n/2 [2a + (n-1)d2]

= n/2 [2 + (n-1)2] (putting a as 1 and d as 2)

= n[1+ (n-1)]

=n²

S3= n/2 [2a + (n-1)d3]

=n/2 [2+ (n-1)3] (putting a as 1 and d as 3)

= n/2[3n-1]

to prove _ S1+S3=2S2

S1+S2

= n/2 [n+1] + n/2[3n-1]

=n/2[n+1+3n-1]

=n/2[4n]

=2n²

=>2S2

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