Question

The sum of first n terms of three arithmetic progressions are s1
s2 and s3 respectively. the first term of each A P is 1 and their common differences are 1,2and 3 respectively. prove that s1+s3=2s2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

sn = n/2 ( 2a+n-1) d )

s1 = n/2 (2×1 + ( n-1 )2

n( n+1)/2

s2 = n/2 (2×1+(n-1)2

=n²

s3=n/2 (2×1 +(n-1)3

n(3n-1)/2

s1+s2= n(n+1) /2 ,n(3n-1)/2

=n( n+1) + n(3n-1) / 2

n( n+1 +3n -1 )/2 =n×4n/2

2n²=2S2