Question

If Sn denotes the sum of first n terms of AP . Prove that S30 = 3× (S20 -S10)

Answer 1

Answer:

HENCE PROVED

Step-by-step explanation:

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

S30=30/2(2a+(30-1)d)

S30=15(2a+29d)--------------------------(1)

substitute S10 and S20 in expanded form

S30 = 3 (20/2(2a+(20-1)d) - (10/2(2a+(10-1)d))

                      =3(10 x 2a+19d) - (5 x 2a+9d)

Simplify this to get

                       =15(2a+29d)-------------------(2)

So, here (1) and (2) are equal

    HENCE PROVED

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