**Q) **Solve the equation for x:

1 + 4 + 7 + 10 + …. + x = 287

**Ans: **

We can see that it is AP with first term a = 1 and common difference d = 3

Let x be the value of n^{th} term and we need to find value of this n^{th} term.

Let’s start from n^{th} term:

The value of n^{th} term = a + (n – 1) d

Hence, x = 1 + (n – 1) 3

x = 3n – 2….. (i)

………………….. (ii)

Next, we know that, sum of n terms S_{n} =

287 = [2 x 1 + (n – 1) 3 ]

574 = n (3n-1)

By substituting value of n from equation (ii)

574 =

(574)(3) = (x + 2) [ (x + 2) – 1]

1722 = (x + 2) (x + 1)

x^{2} + 3 x – 1720 = 0

(x + 43) (x + 40) = 0

Since, value of x ≠ – 43,

**hence x = 40**