Question

If Sn denotes the sum of the first n terms of an AP. Prove that S(30)=3[S(20) - S(10)]​

Answer 1

Answer:

Step-by-step explanation:

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

LHS = S(30) = 30/2(2a+(30-1)d)

= 15(2a+29d)

= 30a + 435d

RHS =

S(20)= 20/2(2a+(20-1)d)

= 10(2a+19d)

=20a+190d

S(10)= 10/2(2a+(10-1)d)

=5(2a+9d)

10a+45d

S(20)-S(10)= 10a+145d

3[S(20)-S(10)]= 30a+435d = RHS

Therefore LHS = RHS.

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