Question

Find the sum of :-

85+80+75+..........+15

(Arithmetic progression) ​

Answer 1

Tn = a + (n-1) d
Tn = 85+ (n-1)(-5)
15 = 85-5n+5
5n = 75
n= 15

Sn = n/2 (a+l)
Sn = 7(85+15)
Sn= 700

Answer 2

Answer:-

Given:

85 + 80 + 75 +... 15 are in AP.

Here,

• a = 85
• d = 80 - 85 = - 5
• aₙ = 15.

We know that,

nth term of an AP (aₙ) = a + (n - 1)d

So,

⟶ 15 = 85 + (n - 1) ( - 5)

⟶ 15 - 85 = - 5n + 5

⟶ 15 - 85 - 5 = - 5n

⟶ - 75 = - 5n

⟶ - 75/ - 5 = n

⟶ 15 = n

Now,

Sum of first n terms of an AP (Sₙ) = n/2 * [ 2a + (n - 1)d ]

Hence,

⟶ S₁₅ = 15/2 * [ 2(85) + (15 - 1)( - 5) ]

⟶ S₁₅ = 15/2 * [ 170 - 70 ]

⟶ S₁₅ = (15/2) * 100

⟶ S₁₅ = 750

∴ The sum of the given AP is 750.