Question

An AP is given by
K, 2K/3, K/3,0,...... .
1. find the sixth term.
2. find the nth term
3. if the 20th term is equal to 15 find K.​

Answer 1

Step-by-step explanation:

1) a = K, d = - K/3, n = 6

An = a + (n - 1)d

An = K + 5×(-K/3)

An = -2K/3

2) nth term......

An = a + (n -1)d

An = K + (n - 1)(-k/3)

An = K - Kn/3 + k/3

An = 4k/3 - kn/3

An = (4-n)k/3

3) A20 = a + 19d = 15

K + 19 × (-K/3) = 15

(3K - 19K)/3 = 15

16K = 15 × 3

K = -45/16

Answer 2

common difference (d) = 2k/3 - k = -k/3

first term (a) = k

6th term = a + 5d

=> k + 5×(-k/3)

=> -2k/3

nth term => k - (n-1) k/3

now given

20th term = 15

a+19d = 15

k - 19 k/3 = 15

-16k/3 = 15

=> k= -45/16

hope it will help you☺️☺️