Answer:In this problem,
a
n
ā
=x
a
1
ā
=1
d=6ā1=5
ā“x=1+(nā1)Ć5
ā“xā1=(nā1)Ć5
ā“(nā1)=
5
xā1
ā
ā“n=
5
xā1
ā
+1
ā“n=
5
xā1+5
ā
ā“n=
5
x+4
ā
Equation (1)
2) Sum of n terms of A.P. is
āa
n
ā
=
2
n
ā
[2a+(nā1)d]
As given in problem, āa
n
ā
=148
ā“
2
n
ā
[2a+(nā1)d]=148
ā“
2
(
5
x+4
ā
)
ā
[(2Ć1)+(
5
x+4
ā
ā1)5]=148
ā“
10
x+4
ā
[2+(
5
x+4ā5
ā
)5]=148
ā“
10
x+4
ā
[2+xā1]=148
ā“
10
x+4
ā
[x+1]=148
ā“(x+4)(x+1)=1480
ā“x
2
+5x+4=1480
ā“x
2
+5xā1476=0
ā“x=
2Ć1
ā5Ā±
(5)
2
ā4Ć1Ć(ā1476)
ā
ā
ā“x=
2
ā5Ā±
25+5904
ā
ā
ā“x=
2
ā5Ā±
5929
ā
ā
ā“x=
2
ā5Ā±77
ā
neglecting negative root, we get,
x=
2
ā5+77
ā
ā“x=
2
72
ā
ā“x=36
Step-by-step explanation: i hope it was helpfu;;
