Question

If 3 + k, 18 – k, 5k + 1 are in A.P. then find k

Answer 1

3 + k, 18 – k, 5k + 1 are in A.P

⇒ 2b = a + c if a, b, c are in A.P
∴ `underbrace(3 + "k")_"a",  underbrace(18 - "k")_"b",  underbrace(5"k" + 1)_"c"`

2b = a + c

⇒ 2(18 – k) = 3 + k + 5k + 1

36 – 2k = 4 + 6k

6k + 2k = 36 – 4

8k = 32

k = `32/8` = 4