Arithmetic Progression

 The sequence  p₁, p₂ ... and q₁, q₂ … are in arithmetic progressions such that p₁ + q₁ = 50 and p₁₁ − p₁₀ = q₉₉ − q₁₀₀. Find the sum of the first 100 terms of the progression, 

( p₁ + q₁),( p₂ + q₂) …

Answer:

The common difference between the 2 sequence is same but one is negative, given p₁₁ − p₁₀ = q₉₉ − q_100. 

negative So, ( p₂ + q₂)  = ( p₁ + q₁) = ( p_n + q_n)

therefore, the sum of the series = 50 x 100 = 5000