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° C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was – 30° Celsius then find the temperature on the other five days.

Let Monday be the first term i.e. a = t₁
Let Tuesday be the second term that is t₂
Let Wednesday be the third term that is t₃
Let Thursday be the fourth term that is t₄
Let Friday be the fifth term that is t₅
Let Saturday be the sixth term that is t₆
Given: t₁ + t₆ = 5 + (t₂ + t₆)
⇒ a = 5 + (t₂ + t₆) – t₆
⇒ a = 5 + t₂ …. (1)
We know that,
Now, by using n^th term of an A.P. formula
t_n = a + (n – 1) d
where n = no. of terms
a = first term
d = common difference
t_n = n^th terms
Thus, t₂ = a + (2 – 1) d
⇒ t₂ = a + d
Now substitute value of t₂ in (1) we get,
⇒ a = 5 + (a + d)
⇒ d = a – 5 – a = – 5
Given: t₃ = – 30°
Thus, t₃ = a + (3 – 1) × (– 5)
⇒ – 30 = a + 2 × (– 5)
⇒ – 30 = a – 10
⇒ a = – 30 + 10 = – 20°
Thus, Monday, a = t₁ = – 20°
Using formula t_{n + 1} = t_n + d
We can find the value of the other terms
Tuesday, t₂ = t₁ + d = – 20 – 5 = – 25°
Wednesday, t₃ = t₂ + d = – 25 – 5 = – 30°
Thursday, t₄ = t₃ + d = – 30 – 5 = – 35°
Friday, t₅ = t₄ + d = – 35 – 5 = 40°
Saturday, t₆ = t₅ + d = – 40 – 5 = – 45°
Thus, we obtain an A.P.
– 20°, – 25°, – 30°, – 35°, – 40°, – 45°