Question

4x4 - 16
The first term
of two A.P.s are equal and the ratios of their coramon
differences is 1 : 2. If the 7th term of first A.P. and 21th term of
second A.P. are 23 and 125 respectively. Find two A.P.S.​

Answer 1

Answer:

we have given that

a =A

and

d/D=1/2

now,

a7=23

A21=125

now,

a +6d=23-------------1

A+20D=125----------2

by elimination method

we get,

20D - 6d = 102

take 2 common

so,

10D - 3d=51 --------- 3

now ,

d/D=1/2

then,

D=2d, put in 3

we get,

10(2d) - 3d= 51

20d - 3d=51

17d=51

d=3

so, D=2(3)

D=6

now,

put values of d in equation 1

we get,

a+6(3)=23

a+18=23

a=23-18

a=5

hence first ap is 5,8,11,14 17,20----------

Now put value of D in equation 2

we get,,

A+20(6)=125

A+120=125

A=125-120

A=5

HENCE SECOND AP IS 5,11,17,23,29,35,41----------

HOPE IT IS VERY HELPFUL FOR YOU