Question

solve the equation 1 + 4 + 7 + 10 ....+x= 287

Answer 1

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Answer 2

 given

a=1

d=4−1=3

and, s  

n

​  

=287

Now,

s  

n

​  

=  

2

n

​  

(2a+(n−1)d)

⇒287=  

2

n

​  

(2×1+(n−1)3)

⇒287=  

2

n

​  

(2+3n−3)

⇒574=n(3n−1)

⇒574=3n  

2

−n

⇒3n  

2

−n−574=0

on solving the quadratic equation using formula

n=  

2a

−b±  

b  

2

−4ac

​  

 

​  

 

We get n=14&  

3

−41

​  

[does not exist]

so, n=14

Now,

s  

n

​  

=  

2

n

​  

(a+1)

⇒287=  

2

14

​  

(1+x)

⇒574=14(1+x)

⇒(1+x)=  

14

574

​  

 

⇒1+x=41

⇒x=41−1

∴x=40

x=40isthesolution.

​