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Y+6=11;x=–2,0,4
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Sagot :

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Answer:In this problem,

a  

n

​

=x

a  

1

​

=1

d=6−1=5

∴x=1+(n−1)×5

∴x−1=(n−1)×5

∴(n−1)=  

5

x−1

​

 

∴n=  

5

x−1

​

+1

∴n=  

5

x−1+5

​

 

∴n=  

5

x+4

​

            Equation (1)

2) Sum of n terms of A.P. is

∑a  

n

​

=  

2

n

​

[2a+(n−1)d]

As given in problem, ∑a  

n

​

=148

∴  

2

n

​

[2a+(n−1)d]=148

∴  

2

(  

5

x+4

​

)

​

[(2×1)+(  

5

x+4

​

−1)5]=148

∴  

10

x+4

​

[2+(  

5

x+4−5

​

)5]=148

∴  

10

x+4

​

[2+x−1]=148

∴  

10

x+4

​

[x+1]=148

∴(x+4)(x+1)=1480

∴x  

2

+5x+4=1480

∴x  

2

+5x−1476=0

∴x=  

2×1

−5±  

(5)  

2

−4×1×(−1476)

​

 

​

 

∴x=  

2

−5±  

25+5904

​

 

​

 

∴x=  

2

−5±  

5929

​

 

​

 

∴x=  

2

−5±77

​

 

neglecting negative root, we get,

x=  

2

−5+77

​

 

∴x=  

2

72

​

 

∴x=36

Step-by-step explanation: i hope it was helpfu;;

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