Question

In an ap (8/3)times of sum of first five terms is equal to the sum of the next five terms. If the first term of the ap is 8 then what will be the common difference

Answer 1

Common difference is 8

Solution is present in attached file

Answer 2

Let a is the first term and d is the common difference of an arithmetic progression.

first five terms are : a , a + d , a + 2d , a + 3d , a + 4d

next five terms are : a + 5d, a + 6d, a + 7d, a + 8d , a + 9d

a/c to question,

(8/3) × [a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) ] = [(a + 5d) + (a + 6d) + (a + 7d) + (a + 8d) + (a + 9d)]

or, (8/3) × [5a + 10d ] = [5a + 35d]

or, (8/3) [a + 2d] = [a + 7d]

or, 8a + 16d = 3a + 21d

or, 5a = 5d

or, a = d

given, first term , a = 8

so, common difference , d = 8