Question

Jagne wale mere sare bhaii or unki Pyare behne krioya krke..kuch Madad ada krde..


My questions are following.
s30=3(s20- s10) ——prove This if..an denotes the first n terms of an AP ..



Only answers by serious users..maths Arya Bhatt’s..and brainliest users like me xD.


No thanks in advance..

Answer 1

sn=n/2(2a+(n-1)d
s30=15(2a+29d)
Now,
s20-s10=10(2a+19d)-5(2a+9d)
Multiplying it with 3

3[20a+190d)-10a+45d]
3[10a+235d]
30a+192d
=s30
Hence proved

Answer 2

Hii

Here is your answer -

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

Sum of the first n terms of an A.P,

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

Then, S(30) = 30/2[2a + (30 - 1)d] ... (i) L.H.S

⇒ S[(20) - S(10)] = 20/2[2a + (20 - 1)d] - 10/2[2a + (10 - 1)d]

⇒ S[(20) - S(10)] = 10[2a + (20 - 1)d] - 5[2a + (10 - 1)d]

⇒ S[(20) - S(10)] = 10a + 190d  -  45d .

⇒ S[(20) - S(10)] = 3(10a + 145d)

⇒ S[(20) - S(10)] = 3 × 5(2a + 29d )

⇒ S[(20) - S(10)] = 30/2[2a + (30 - 1)d] ... (ii) R.H.S

From (i) and (ii), we get

S(30) = 3[S(20) - S(10)]

Hence Proved.