Question

If the sum of first p term of an A.P. is $ap^{2}$ + bp, find its common difference.

Answer 1

Answer:

The common Difference is 2a .

Step-by-step explanation:

Given :  

Sp = ap² + bp……….(1)

On putting n = 1 in eq (1),

S1 = a(1)² + b(1)

S1 = a + b  

 

On putting n = 2in eq (1),

S2 = a(2)² + b(2)

S2 = a × 4 + 2b

S2 = 4a + 2b

 

a2 = S2 - S1

[nth term of the A.P., an = Sn – S(n – 1)]

a2 = 4a + 2b - (a + b)

a2 = 4a + 2b - a - b

a2 = 4a - a + 2b - b

a2 = 3a + b

Common  difference , d = a2 - a1  

d = 3a + b – (a + b)

d = 3a + b - a - b

d = 2a

Hence,the common Difference is 2a .

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Answer 2

Step-by-step explanation:

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