# If Sn Denotes the Sum of First N Terms of an A.P., Prove that S30 = 3[S20 − S10] - Mathematics

If Sn denotes the sum of first n terms of an A.P., prove that S30 = 3[S20S10]

#### Solution

We know

Sn=n/2[2a+(n1)d]

S20=20/2[2a+(201)d] and S10=10/2[2a+(101)d]

S20=10[2a+19d] and S10=5[2a+9d]

S20=20a+190d and S10=10a+45d

3(S20S10)=3(20a+190d10a45d)

= 3(10a+145d)

= 15(2a+29d)

=30/2[2a+(301)d]

= S30

∴ S30=3(S20S10)

Concept: Sum of First n Terms of an AP
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