Question

find the value of x , when in the AP given below
2+6+10+...+x=1800

Answer 1

2+6+10+_1782_+×=1800

Answer 2

In the given AP,

Sum of x terms =1800

First term,a1 =2

Second term,a2 =6

Then, Common difference,d=a2-a1=6-2=4

Using Sn formula ,

Sn =

$\frac{n}{2}(2a + (n - 1)d)$

Putting value of Sn,d,a1;

1800=

$= \frac{n}{2} (2 \times 2 + (n - 1)4)$

then,

1800×2 = n(4+4n-4)

$3600 = 4n {}^{2} + 4n - 4$

take 4 as common,

$3600 = 4(n { + n - 1)}^{2}$

$\frac{3600}{4} = {n}^{2} + n - 1$

we get,

$900 = {n}^{2} + n - 1$

That is,

${n}^{2} + n - 901 = 0$

when we solve this we get the value of n which is,

n = x

Hence we get value of x..