arithmetic progression?

Question

i read a math like below

in any A.P a1,a2,a3 we know 2a2=a1+a3
similarly, a1+a5=2a3 , a3+a9=2a6

can you tell, how a1+a5=2a3 and a3+a9=2a6 ?

they are quite far apart unlike consecutive a1,a2,a3

please explain

Answer 1

An arithmetic progression is a sequence such that the difference between any two consecutive entries is a constant. Call it k...

a2 = 1a + k
a3 = a2 + k = a1 + 2k
a4 = a3 + k = a2 + 2k = a1 + 3k

This should be enough to allow you to prove all of your given assertions.