" ... the sum of the first five terms is one-fourth of the next terms."
confusing, I will assume you meant:
the sum of the first five terms is one-fourth of the next term.
i.e.
the sum of the first five terms is one-fourth of the 6th terms.
a = 2
6th term = a+5d
sum(5) = (5/2)(2a + 4d) = (5/2)(4 + 4d)
= 10 + 10d
10 + 10d = (1/4)(a+5d)
40 + 40d = 2 + 5d
35d = -38
d = -38/35
term(12) = a + 11d
= 2 - 11(-38/35) ≠ -112
check the wording of your question.
working backwards:
if a = 2 and term(20) = -112
term(20) = a+19d
2 + 19d = -112
19d = -114
d = -6
so the sum of the first five terms would be
(5/2)(4 + 4(-6)) = -50
Now that is supposed to be 1/4 of "something"
In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next terms. Show that 20th term is -112.
1 answer