An Ap is given by K,2k/3,K/3,0.....Find the 6th term, Find the nth term. If the 20th term is equal to 15 find K

Answer 1

common difference = 2k/3 - k = -k/3

given: 20th term is 15
so k + 19(-k/3) = 15
times 3, (I don't like fractions)

3k - 19k = 45
k = - 45/16

first term is -45/16
common difference = -k/3 = 15/16

term 6 = a + 5d
= -45/16 + 5(15/16) = 15/8

term n = a + (n-1)d = a + nd - d
= -45/12 + (15/16)n - 15/16
= -75/16 + (15/16)n
or
= 15(n - 5)/16 or .... (15/16)(n-5)

take your pick