Question

The 18 term of AP is halh of its 2 term and the 11 term .term exceeds one third of its 4 term by 1.find the 15 term.

Answer 1

i)
let first term of AP = a
and common differece =d 

18 term =1/2*2nd term

a+17d = 1/2*(a+d)

2(a+17d) = a+d
2a+17d -a-d=0

a+16d=0------(1)

ii)11th term = 1/3*4th term +1

a+10d = 1/3(a+3d) +1

a+10d =( a+3d+3)/3

3(a+10d) = a+3d+3

3a+30d-a-3d=3

2a+27d=3-----(2)
multiply equation (1) with 2 and subtract (2) from it

2a+32d=0
2a+27d=3
--------------------
0+5d =3

d= 3/5

substitute d value in (1)

a+ 16*3/5=0

a+48/5

a= -48/5

iii) 15th term = a+14d

= -48/5 + 14*3/5

= -48/5+42/5
=-6/8