Question

in an ap the first term is 2 and the sum of 1st five terms is 14 of the sum of next 5 terms. show that 20th term is - 112​

Answer 1

$\textit{ANSWER:}$

$<b>Given, first term = a = 2 Let the common difference be d. Given, the sum of first five terms is one-fourth of the next five terms, => [a + (a+d) + (a+2d) + (a+3d) + (a+4d)] = 1/4[(a+5d) + (a+6d) + (a+7d) + (a+8d) + (a+9d)] => (5a + 10d) = 1/4(5a + 35d) => 20a + 40d = 5a + 35d => 15a + 5d = 0 => 3a +d = 0 => d = -3a = -6 The 20th term = a + (20–1)d = a + 19d = 2 + (19*(-6)) = 2 - 114 = -112 The 20th term of the given AP is -112.$