The ratio of sum of first 6 terms to the sum of first 10 terms in AP i

1.	The ratio of sum of first 6 terms to the sum of first 10 terms in AP is 3:7 anda=3a-4. Find the progression.
Answer» S6 = 6/2(2a + 5d)S10 = 10/2(2a + 9d) Now,S6/S10 = 3/73(2a + 5d)/5(2a + 9d) = 3/721(2a + 5d) = 15(2a + 9d)14a + 35d = 10a + 45d4a = 10dd = 2a/5........(1) Given,a16 = 3a - 4a + 15d = 3a - 4 Put value of d from eq (1)a + 152a/5 = 3a - 4a + 6a = 3a - 44a = - 4a = - 1 d = 2-1/5 = - 2/5 Therefore, AP isa, a + d, a + 2d........-1, (-1 + - 2/5), (-1 + - 4/5).....-1, - 7/5, - 9/5.....

The ratio of sum of first 6 terms to the sum of first 10 terms in AP is 3:7 anda=3a-4. Find the progression.

Answer»

S6 = 6/2(2a + 5d)S10 = 10/2(2a + 9d)

Now,S6/S10 = 3/73(2a + 5d)/5(2a + 9d) = 3/721(2a + 5d) = 15(2a + 9d)14a + 35d = 10a + 45d4a = 10dd = 2a/5........(1)

Given,a16 = 3a - 4a + 15d = 3a - 4

Put value of d from eq (1)a + 15*2a/5 = 3a - 4a + 6a = 3a - 44a = - 4a = - 1

d = 2*-1/5 = - 2/5

Therefore, AP isa, a + d, a + 2d........-1, (-1 + - 2/5), (-1 + - 4/5).....-1, - 7/5, - 9/5.....