Question

if the sum of first P terms of an ap is ap^2 + bp^2 find its common difference

Answer 1

Given that the sum of p terms of an AP is ap2 + bp .

Now, Put p = 1,2,3,......

S 1 = a(1)2 + b(1)

S1 = a + b = a 1

S2 = a(2)2 + b(2)

S2 = 4a + 2b

Now, S2 = a1 + a 2

4a + 2b = a + b + a 2

4a + 2b - a - b = a 2

3a + b = a 2

Common difference, d = a2 - a1

d = 3a + b - (a + b)

d = 3a + b - a - b

d = 2a

Therefore, the common difference of the given AP is 2a.

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