Question

1+4+7+10.......+x=287 find x

Answer 1

Here, a=1

d=3

Sn=287

An=?=x

Sn=n/2[2a+(n-1)d]

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 ☺