Question

If P Q R are three consecutive terms of an AP than Q will be _____ of p and r
Mean
Median
Sum

Answer 1

mean is the answer of your question

Answer 2

Answer:

Mean of P and Q

Step-by-step explanation:

We can prove this,

Let the first term be 'a' and have a common difference of 'd'

a1 = a

a2 = a + d

a3 = a + 2d

Now if we add a3 and a1 we get

a + 2d + a

= 2a + 2d = 2(a + d)

But we know that (a + d) = a2

a1 + a3 = 2 × a2

Thus,

a2 = (a1 + a3)/2

That is,

The 2nd term is the arithmetic mean of 1st and the 3rd term.

This can be true for any 3 consecutive terms like a6 = (a5 + a7)/2

Therefore this is not a theorem but an observation, but it is a universal truth and was there even before the experiments and observations were done

Hope you understood it........All the best