Question

If 9k – 6, 5k – 4, 6k – 17 are in AP then the value of k is
A. -3
B. -11
C. 3
D. 10

Answer 1

Hint: If three numbers a, b and c are in AP the difference between b, a and c, b are the same.
That is, b – a = c – b. Using these equations, we can find the value of k.

Complete step-by-step answer:

In this question it is given that 9k – 6, 5k – 4 and 6k –17 is in AP.
A sequence a, b, c is called an arithmetic progression (A.P.), if the difference between any term and its previous term is always the same. i.e.,
b – a = c – b = constant.
This constant is called the common difference and it is represented as ‘d’.
Now considering,
a = 9k – 6
b = 5k – 4
c = 6k –17
we have,
b – a = c – b = constant ...........(i)
Applying equation (i) we have,
(5k – 4) – (9k – 6) = (6k – 17) – (5k – 4) .............(ii)
On solving equation (ii) we can get the value of k.
Now, on simplifying equation (ii) we get,
5k – 4 – 9k + 6 = 6k – 17 – 5k + 4
5k – 4 – 9k + 6 = 6k – 17 – 5k + 4
5k – 9k – 4 + 6 = 6k – 5k + 4 – 17
– 4k + 2 = k– 13
k + 4k = 2 + 13
5k =15
k = 3
Hence, the value of k = 3.
Therefore, the correct answer is option C.

Note: In this question it is given that 9k – 6, 5k – 4, 6k – 17 are in AP. There are chances that instead of finding the difference between 5k – 4 and 9k – 6, the student might find the difference between 9k – 6 and 5k – 4, which may lead to a wrong answer. This can also happen in finding the difference between 5k – 4 and 6k – 17. Instead of finding the difference between 6k – 17 and 5k – 4, the student might find the difference between 5k – 4 and 6k – 17, which may also lead to a wrong answer. Hence it should be noted that the difference should be found between any term and its previous term only.