Question

If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
A. ab/2(b-a)
B. ab/b-a
C. 3ab/b-a
D. none of these

Answer 1

Answer:

A answer is correct form

Answer 2

sum of n term of given AP is 3ab/2(b - a)

given, first term of a ap = a

second term of the ap = b

so, common difference = b - a

and last term of the ap = 2a

last term = Tn = a + (n - 1)d

⇒2a = a + (n - 1)(b - a)

⇒(2a - a) = (b - a)n + (a - b)

⇒b/(b - a) = n ........(1)

now sum of n terms = n/2 [first term + last term ]

= b/(b - a)/2 [a + 2a ]

= 3ab/2(b - a)

hence, sum of n term of given AP is 3ab/2(b - a)

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