Question

find the common difference of an ap whose first term is 1 and the sum of first four terms is one third of the sum of the next four terms

Answer 1

★given first term of A.P ,a = 1

let " d " is the common difference

sum of first four terms = 1/ 3rd of the sum of next 4 terms.

a + a+d + a +2d + a+3d = 1 / 3( a + 4d + a + 5d + a +6d + a + 7d )

( 4a + 6d ) = 1 / 3 ( 4a + 22d )

3 ( 4a + 6d ) = 1 ( 4a + 22d )

12a + 18d = 4a + 22d

12a - 4a = 22d - 18d

8a = 4d

given , a = 1

so now ,

8( 1 ) = 4 d

d = 8 / 4 = 2

d = 2

hence the common difference (d) = 2

【 hope it helps 】