Question

in an ap whose 1st term is 4 the sum first five term is one third the sum of the next five terms find the sum of the 25 terms​

Answer 1

a = 4

S5 = 1/3(S10)

5/2(2a+4d) = 1/3(10/2(2a+9d)

a+2d = 1/3(2a+9d)

3(a+2d) = (2a+9d)

3a+6d = 2a+9d

3a-2a +6d-9d = 0

a-3d = 0

4-3d = 0

d= 4/3

S25 = 25/2(2(4) + 24(4/3)

= 25/2(8+24)

= 25/2(32)

= 25(16)

= 400