Question

If 2p, p+10 , 3p+2 are in AP then find p.

Answer 1

Answer:

If 2p, p+10 , 3p+2 are in AP then p is 6.

Step-by-step explanation:

If numbers are in AP then its common difference is the same.

If the numbers a, b and c are in AP, then. b - a = c-b.

⇒2b = a + c

In given AP a = 2p, b= p+ 10 and c = 3p + 2

Put values on 2b = a + c

2(p+ 10) = 2p+ 3p + 2

2p + 20 = (2 + 3)p + 2

2p + 20 = 5p + 2

2p - 5p = 2 - 20

- 3p = - 18

p = 18/3

p = 6

So, value of p is 6.

Answer 2

Given:

The terms 2p, p+10, and 3p+2 are in Arithmetic Progression.

To Find:

The value of p is?

Solution:

The given problem can be solved using the concepts of Arithmetic Progressions.

1. Let A1, A2, A3, A4, .., An be n consecutive terms on an Arithmetic Progression.

=> According to the concepts of A.P,

=> A2 - A1 = A3 - A2 = A4 - A3 = A5 - A4 = .... = An - (An - 1)

2. Using the above relation, the value of p can be solved,

=> p + 10 - 2p = 3p + 2 - (p + 10), ( As the three terms are consecutive )

=> p + 10 - 2p = 3p + 2 - p - 10,

=> -p + 10 = 2p - 8,

=> 3p = 10 + 8,

=> 3p = 18,

=> p = 18/3,

=> p = 6.

3. Therefore, the three terms are 12, 16, and 20.

Therefore, the value of p is 6. The three consecutive terms are 12, 16, and 20 respectively.