Question

if the sum of first m terms of an A.P is am²+bm ,find its common difference

Answer 1

this is Ur required result

Answer 2

Step-by-step explanation:

2a+2b

Step-by-step explanation:

Given : S_m =am^2+bmS

m

=am

2

+bm

To find:Common difference

Solution:

S_m =am^2+bmS

m

=am

2

+bm

Substitute m = 1

S_1 =a(1)^2+b(1)S

1

=a(1)

2

+b(1)

S_1 =a+bS

1

=a+b

Thus the first term is a+b

Now substitute m =2

S_2 =a(2)^2+b(2)S

2

=a(2)

2

+b(2)

S_2 =4a+2bS

2

=4a+2b

Thus the sum of first two terms is 4a+2b

Second term = Sum of first two terms - first term

Second term = 4a+2b-a-b4a+2b−a−b

= 3a+b3a+b

Common difference = second term - first term

= 3a+b -(a+b)

= 2a+2b

Hence the common difference is 2a+2b