Question

Find the value of x if 2 + 7 + 12 +17+...... + x = 156.

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Answer 1

Answer:

The value of x is 37

Step-by-step explanation:

Given:

$2+7+12+...........+x=156$

clearly it is an A.P

Here,

First term, a=2

Common difference, d=5

Last term, l=x

Then,

$\text{Number of terms of the A.P }\\\\\boxed{\bf\;n=\frac{l-a}{d}+1}$

$\implies\;n=\frac{x-2}{5}+1$

$\implies\;n=\frac{x-2+5}{5}$

$\implies\;n=\frac{x+3}{5}$

$\text{Sum of n terms of the A.P }\\\\\boxed{\bf\;S_n=\frac{n}{2}[a+l]}$

$\implies\;S_n=156$

$\implies\;\frac{x+3}{10}[2+x]=156$

$\implies(x+3)(x+2)=1560$

$\implies\;x^2+5x+6=1560$

$\implies\;x^2+5x-1554=0$

$\implies\;(x+42)(x-37)=0$

$\implies\;x=-42,\:37$

$\text{since the A.P is increasing, the last term cannot be negative}$

$\implies\bf\;x=37$

Answer 2

Answer:

37

Step-by-step explanation:

I hope it helps you

thank you