Question

If Sn denotes the sum of first n terms of an A.P., then S2-S1 is​

Answer 1

Question :- If Sn denotes the sum of first n terms of an A.P., then S2 - S1 is ?

Solution :-

Let ,

• a = first term of AP .
• d = common difference .

we know that,

• sum of n terms of an AP = (n/2)[2a + (n - 1)d]

So, we get,

→ S1 = (1/2)[2a + (1 - 1)d]

→ S1 = (1/2)[2a + 0d]

→ S1 = (1/2)[2a]

→ S1 = a .

Similarly,

→ S2 = (2/2)[2a + (2 - 1)d]

→ S2 = 1[2a + d]

→ S2 = (2a + d)

Therefore,

→ S2 - S1

→ (2a + d) - a

→ 2a - a + d

→ (a + d)

Or,

→ a + 1*d

→ a + (2 - 1)d

comparing with Tn = a + (n -1)d

→ (a2.) (Ans.)

Hence, (S2 - S1) is Equal to a2(second Term of AP.)