Question

show that the sum of an A.P is equal i Sn =(a+b (b+c-2a)÷2(b-a)​

Answer 1

Answer:

first term = a

second term = b

last term = c

so, common difference = (b-a)

now, let last term be the Nth term of the AP

L = a + (n-1) d

=> c = a + (n-1) (b-a)

=> c = a + nb -an -b +a

=> c = 2a -an +nb -b

=> c = 2a -b +nb -an

=> n = (b+c-2a) / (b-a)

now, 

Sn = n/2 (first term + last term)

=> Sn= (b+c-2a)(a+b)/2(b-a)

Answer 2

hi mate

Step-by-step explanation:

first term =a

second term =b

last term = c

so, common difference = (b-a) .

now, let last term be the Nth term of the AP.

L= a+ (n-1) d

c= a+ (n-1)(b-a)

c= a+ nb-an -b+a

c= 2a -b +nb - an

n= b+c-2a / b-a

now ,

sn = n/2 ( first term + last term).

sn =( b+c-2a )(a+b) /2(b-a) .