Question

In an ap the first term is 2 and the sum of the first five terms is one fourth of sum of next 5 terms find the sum of first 20 terms

Answer 1

Answer:

Step-by-step explanation:

Given, first term = a = 2

Let the common difference be d.

Given, the sum of first five terms is one-fourth of the next five terms,

=> [a + (a+d) + (a+2d) + (a+3d) + (a+4d)] = 1/4[(a+5d) + (a+6d) + (a+7d) + (a+8d) + (a+9d)]

=> (5a + 10d) = 1/4(5a + 35d)

=> 20a + 40d = 5a + 35d

=> 15a + 5d = 0

=> 3a +d = 0

=> d = -3a = -6

The 20th term = a + (20–1)d = a + 19d = 2 + (19*(-6)) = 2 - 114 = -112

The 20th term of the given AP is -112