Question

Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was $5^{\circ }C$ more than sum of temperatures of Tuesday and Saturday. If the temperature of Wednesday was $-{30}^{\circ }C$ celsius then, find the temperature on the other five days.

Answer 1

In A.P,

​Let, first term $=a$​

common difference $=d$

The terms of A.P are $a_1=a,a_2=(a+d),a_3=(a+2d),a_4=(a+3d),a_5=(a+4d)\dots$

The readings of the temperature (Temp.) were in A.P.
Let the Temp. of Monday, $a_1=a$
Temp. of Tuesday, $a_2=a+d$
Temp. of Wednesday, $a_3=a+2d$
Temp. of Thursday, $a_4=a+3d$
Temp. of Friday, $a_5=a+4d$
Temp. of Saturday, $a_6=a+5d$
The sum of temperatures of Monday and Saturday was $5^{\circ }C$ more than the sum of temperatures of Tuesday and Saturday.
$a_1+a_6=5+a_2+a_6$

$\therefore a+(a+5d)=5+(a+d)+(a+5d)$

$\Rightarrow 2a+5d=5+2a+6d$

$\Rightarrow 6d-5d=-5$

$\Rightarrow d=-5$
Also, the temperature of Wednesday was $-{30}^{\circ }C$.
$\therefore a+2d=-30$

$\Rightarrow a+2\times (-5)=-30$

$\Rightarrow a-10=-30$

$\Rightarrow a=-30+10$

$\Rightarrow a=-20$
Hence, the temperature on the other five days was:
Monday $=a=-{20}^{\circ }C$
Tuesday $=(a+d)=-{25}^{\circ }C$
Thursday $=(a+2d)=-{30}^{\circ }C$
Friday $=(a+3d)=-{35}^{\circ }C$
Saturday $=(a+4d)=-{40}^{\circ }C$