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 i.e t₂

Let Wednesday be the third term i.e t₃

Let Thursday be the fourth term i.e t₄

Let Friday be the fifth term i.e t₅

Let Saturday be the sixth term i.e 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°