M4maths Previous Puzzles

25 Feb 2022 Sequence & Series

Fractions 1/(x+9) , 1/(x+13) and 1/(x+21) are in arithmetic progression, then x=?

OPtion

1) 8
2) 10
3) 7
4) 3
5) 4
6) 5
7) 6
8) 12
9) 2
10) None of these

Solution

For an A.P. difference between two consecutive terms is same.
.'. 1/(x+9) - 1/(x+13) = 1/(x+13) - 1/(x+21)
[(x+13) - (x+9)] / [(x+9)(x+13)] = [(x+21) - (x+13)] / [(x+13)(x+21)]
4/(x+9) = 8/(x+21)
x = 3

Correct Option: 4 Best Solution (5)

G.S.Kantharao   2 years AGO

2/(x+13)=1/(x+9)+1/(x+21)
2/x+13=(x+21)+(x+9)/(x^2+30x+189)
2(x^2+30x+189)
=2x^2+56x+390
60x-56x=390-378=12
4x=12=>x=3
So my option is 4👈

Like? Yes (7) | No   

Mayank Kandoi   2 years AGO

1/(x+9) + 1/(x+21) = 2/(x+13)
By solving, we get x = 3

Like? Yes (3) | No   

RAMADURAI NATESAN   2 years AGO

Since the 3 terms are in A.P.,
1/x+13 - 1/x+9 = 1/x+21 - 1/x+13. Solving,
x = 3

Like? Yes | No   

ANOOP R   2 years AGO

since these terms are in AP, 1/(x+13)- 1/(x+9) = 1/(x+21)- 1/(x+13) implies finally Quadratic equation
x^2 + 10x-39= 0
implies-- (x+13) * (x-3)=0
i.e, either x=-13 or x=3
but since one term here is 1/(x+13), if we put x=-13, it will become 1/0 which is not possible. hence x=3.

Like? Yes | No   

Pargat Pal Singh   2 years AGO

1/(x+13)- 1/(x+9) = 1/(x+21)- 1/(x+13)
solving it, we get
x=3

Like? Yes (4) | No (5)