Question

Solve the equation: 1 + 4 + 7 + 10 + .......+ x = 287.​

Answer 1

Sn = n/2(2a+(n-1)d)  given a=1, d=4-1=3 & Sn = 287

287 = n/2 (2*1 +(n-1) 3)  

287*2 = n(2 + 3n - 3)

574 = 2n + 3n^2 - 3n

3n^2 -n - 574 = 0

on solving the quadratic equation using formula n= -b + sq.root(b^2 -4ac)

                                                                           -----------------------

                                                                                         2a

we get   n = 14,  -41/3  n not equal to  -41/3 due to negative nos.

n=14

Sn = n/2 (a +l)

287 = 14/2(1 +x)

574 = 14 (1+x)

574 / 14 = 1+x

41 = 1 + x

So, x = 41 - 1

     x = 40 is the solution

Answer 2

Either ..... or x should not be there

I think so

X = 265