Question

if -10, p,q,20 are in AP find P and Q​

Answer 1

Answer:

p = 0

a = 10

Step-by-step explanation:

$- 10 \: \: \: \: \: \: p \: \: \: \: \: \: \: q \: \: \: \: \: \: 20 \\ \\ 20 = - 10 + 3d \\ \\ 30 = 3d \\ \\ d = 10 \\ \\ therefore \: \: \: p = - 10 + 10 = 0 \\ \\ and \: \: \: q = - 10 + 2(10) = 10$

Answer 2

Required Answer:-

If -10, p, q and 20 are in A.P. then the common difference between two consecutive terms is always the same. Hence,

=> p - (-10) = q - p = 20 - q

=> p + 10 = q - p = 20 - q

Equating differently now,

=> p + 10 = q - p

=> 2p = q - 10

=> 2p - q = -10 -----(1)

And,

=> q - p = 20 - q

=> 2q - p = 20 -------(2)

Multiplying (1) with 2,

=> 4p - 2q = -20

Now adding both the equations$,$

=> 4p - 2q + 2q - p = 0

=> 3p = 0

=> p = 0

Then, q = 0 + 10 = 10

Thus,

The required values of p and q are 0 and 10 respectively.