Question

If p – 1, p + 3 and 3p – 1 are in AP. Then the value of p will be,
A. 4
B. – 4
C. 2
D. – 2

Answer 1

Hint:- We had to only use the condition that the difference of two consecutive terms of an AP are always equal and is known as the common difference of the AP.

Complete step-by-step answer:

Now as we know that the p – 1, p + 3 and 3p – 1 are in AP.
And according to the condition of AP if the terms a, b and c are in AP then the difference of the two consecutive terms must be equal and is known as the common difference i.e. b – a = c – b = common difference of the AP.
So, now we can apply this condition in the given AP.
So, (p + 3) – (p – 1) = (3p – 1) – (p + 3) (1)
Now we had to solve the above equation to find the value of p.
So, opening the brackets in the above equation. We get,
p + 3 – p + 1 = 3p – 1 – p – 3
4 = 2p – 4
So, adding 4 to both the sides of the above equation. We get,
2p = 8
Dividing both sides of the above equation by 2. We get,
p = 4
Hence, the correct option will be A.

Note:- Whenever we come up with this type of problem then there is also another method to find the value of p and that is, we can also use the condition that if three terms a, b and c are in AP then the middle term i.e. b can also we written as b = 2(a + c). So, we can form the equation by applying this condition in the given AP and then after solving that equation we will get the required value of p.