Question

if the sum of first p term of an ap is (ap²+bp) find its common difference​

Answer 1

Step-by-step explanation:

Given that the sum of p terms of an AP is ap

2

+bp

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

S

p

=ap

2

+bp

⇒ S

1

=a(1)

2

+b(1)

∴ S

1

=a+b

⇒ S

2

=a(2)

2

+b(2)

∴ S

2

=4a+2b

∴ a

1

=S

1

=a+b

∴ a

2

=S

2

−S

1

=4a+2b−(a+b)

=4a+2b−a−b

=3a+b

∴ Common difference =d

⇒ d=a

2

−a

1

⇒ d=3a+b−(a+b)

⇒ d=3a+b−a−b

∴ d=2a