Question

14. In an A.P ratio of 4th term and 6th term is 5:8 and the sum of 7 terms is 70. Find
the A.P​

Answer 1

Answer:

please check the image

Answer 2

given,

4th term , a4 = a +( n-1)d = a+ 3d

6th term, a6 = a +( n-1)d = a+5d

a4 / a6 = 5 / 8

thus,

a+3d / a+ 5d = 5/8

8(a+3d) = 5( a+5d)

8a + 24d = 5a + 25d

3a = d

thus,

d= 3a ......(1)

and,

S7= 70

S7 = n/2[ 2 a + (n-1)d]

S7 = 7/2 [ 2a + 6d]

S7 = 7[ a+3d]

S7 = 7a +21d

=> 70 = 7a +21 d

divide by 7,

10 = a + 3d

substituting value of d as 3a,

10 = a + 9 a

10 = 10 a

and , a= 1

thus, d= 3a =3

A.p =

a, a+d ,a+2d , and so on....

=> 1 , 4 , 7 , 10, ......