Question

the sum of n,2n,3n term of an Ap is s1,s2,s3,respectively than prove that s3=3 (s2-s1

Answer 1

I hope this answer would be helpful for you

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let a be the first term and d be the common difference of the given A.P.

Then, S(1) = n/2[2a + (n - 21)d]

S(2) = 2n/2[2a + (2n - 1)d]

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

Again,

3[S(2) - S(1) = 3{2n/2[2a + (2n - 1)d] - n/2[2a + (n - 1)d}

= 3{n/2[4a + 2(2n - 1)d] - [2a + (n - 1)d}

= 3[n/2(4a + 4nd - 2d - 2a - nd + d]

= 3[n/2(2a + 3nd - d]

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

= S(3)

L.H.S = R.H.S

Hence, Proved.

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