Question

Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.

Answer 1

We have been given an A.P

2+6+10+...+x=1800

a = 2, d = 6 - 2 = 4, `a_n = x  "and"  s_n = 1800`

Firstly, we will find using

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

`1800 = n/2[2 xx 2 + (n - 1)4]`

`1800 = (4n + 4n^2 - 4n)/2`

`900 = n^2`

⇒ n = ±30

Number of terms can not be negative

n = 30

Now for value of x which is `a_n`

`a_n = a + (n - 1)d`

`x = 2 + (30 - 1)4`

x = 2 + 116

x = 118

Therefore, value of x is 118.