Question

solve the equation 2+5+8+11+...........+x=345

Answer 1

here is ur answer...

Answer 2

Answer: The value of x is 44.

Step-by-step explanation:

Since we have given that

$2+5+8+11+........+x=345$

Let a = 2

d = 5 - 2 =3 (common difference)

First we find the number of terms:

$a_n=a+(n-1)d\\\\x=2+(n-1)3\\\\x=2+3n-3\\\\x=3n-1\\\\x+1=3n\\\\\dfrac{x+1}{3}=n$

Since Sum of n terms = 345

So, our equation becomes,

$345=\dfrac{n}{2}(2+x)\\\\345\times 2=n(2+3n+1)\\\\690=n(3n+3)\\\\690=3n^2+3n\\\\230=n^2+n\\\\n^2+n-230=0\\\\n=15\ and\ 15.33333\\\\So,\ n=15$

So, x = 3n-1

$x=3\times 15-1\\\\x=45-1\\\\x=44$

Hence, the value of x is 44.