Question

Solve the equation 2+5+8...+x=155

Answer 1

Answer:

Step-by-step explanation:

2 + 5 + 8 + ......... +x = 155

first term a = 2 ; common difference d = 3

a_n = a+(n-1)d = 155

2 + (n - 1)3 = 155

2+3n - 3 = 155

3n = 156

n = 156/3 = 52 then n = 52 is in a_n

2 + (52 - 1)3 = 155

2 + 153 = 155 then x =51

Answer 2

from lhs, we find that the given series are in ap whose last term is x.

let this term is the nth term of the given series in LHS.

therefore, tn =x

a+(n-1)d =x, where a is the first term of the given series.

2+(n-1)3 =x

2+3n-3=x

3n-1=x

3n=x+1

$n = \frac{x + 1}{3}$

therefore, 2+5+8+..........+x=

$\frac{ x + 1}{6} (2 + x)$

Hence

$\frac{x + 1}{6} ( x + 2) = 155$

${x}^{2} + 3x + 2 = 930$

${x}^{2} + 3x - 928 = 0$

${x}^{2} + 32x - 29x - 928 = 0$

$(x + 32)(x - 29) = 0$

x=-32,29

But here x=-32 which is not possible.

Therefore, x=29.