Question

A finite arithmetic progression has 20 terms.The sum of the first 6 terms of the progression is equal to −12, and the sum of the last 8 terms of the progression is equal to −224. Find the initial term and the common difference d

Answer 1

Answer:

Initial term = 3 & common difference = - 2

Step-by-step explanation:

Let the initial term T₁ = a & the common difference = d

Then the 6th term T₆ = a + (6 - 1) d = a + 5d

13th term T₁₃ = a + 12d

20th term T₂₀ = a + 19d

Therefore , the sum of the first 6 terms

S₆ = 6/2 [T₁ + T₆] = 3 [a + a + 5d] = 6a + 15d = - 12 ----- (1)

& the sum of the last 8 terms

S₈ = 8/2 [T₁₃ + T₂₀] = 4 [a + 12d + a + 19d] = 8a + 124d = - 224 --------- (2)

Solving equation (1) & (2) we get

a = 3

d = - 2