Question

please answer.............​

Answer 1

here, common difference is -3

first term ,a=-4

nth term is x

sum of the nth term =437

use formula,

Sn=n/2{a+an}

Answer 2

Answer:

x = 50

Step-by-step explanation:

Here, -4, -1, 2,......, x   is an AP.

$a = -4 \\ \\ d = -1 - (-4) = -1 + 4 = 3$

Here, d = +3. So the terms are in increasing order.

So we can say that x, the last term, is greater than -4, the first term.

∴ x > -4

x  is the  nth term.

$n = \frac{a_n-a}{d}+1=\frac{x-(-4)}{3}+1=\frac{x+4}{3}+1=\frac{x+4+3}{3}=\frac{x+7}{3}$

$S_n=437 \\ \\ \frac{n}{2}[a+a_n]=437 \\ \\ \frac{\frac{x+7}{3}}{2}[-4+x]=437 \\ \\ \frac{x+7}{6}[x-4]=437 \\ \\ \frac{(x+7)(x-4)}{6}=437$

$(x+7)(x-4)=437 \times 6 \\ \\ (x+7)(x-4)=2622 \\ \\ x^2+3x-28=2622 \\ \\ x^2+3x-28-2622=0 \\ \\ x^2+3x-2650=0$

$a=1\ \ \ ; \ \ \ b=3\ \ \ ; \ \ \ c=-2650 \\ \\ \\ b^2-4ac \\ \\ 3^2-(4 \times 1 \times 2650) \\ \\ 9-(-10600) \\ \\ 9+10600 \\ \\ 10609$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-3\pm\sqrt{10609}}{2 \times 1} \\ \\ x=\frac{-3\pm103}{2} \\ \\ x=\frac{100}{2} \ \ \ \ \ OR \ \ \ \ \ x=\frac{-106}{2} \\ \\ x=50 \ \ \ \ \ \ OR \ \ \ \ \ x=-53$

As x > -4, x ≠ -53

∴ x = 50

Hope this may be helpful.

Thank you. Have a nice day. :-)

#adithyasajeevan